Publications by All QDev staff
 2021

Topological van Hove singularities at phase transitions in Weyl metals 
Abstract
 We show that in threedimensional (3D) topological metals, a subset of the van Hove singularities of the density of states sits exactly at the transitions between topological and trivial gapless phases. We may refer to these as topological van Hove singularities. By investigating two minimal models, we show that they originate from energy saddle points located between Weyl points with opposite chiralities, and we illustrate their topological nature through their magnetotransport properties in the ballistic regime. We exemplify the relation between van Hove singularities and topological phase transitions in Weyl systems by analyzing the 3D Hofstadter model, which offers a simple and interesting playground to consider different kinds of Weyl metals and to understand the features of their density of states. In this model, as a function of the magnetic flux, the occurrence of topological van Hove singularities can be explicitly checked.
Pierpaolo Fontana, Michele Burrello, Andrea Trombettoni Journal reference: Phys. Rev. B 104, 195127 (2021) [pdf] DOI: 10.1103/PhysRevB.104.195127

Scalable platform for nanocrystalbased quantum electronics 
Abstract
 Unlocking the full potential of nanocrystals in electronic devices requires scalable and deterministic manufacturing techniques. A platform offering promising alternative paths to scalable production is microtomy, the technique of cutting thin lamellae with large areas containing embedded nanostructures. This platform has so far not been used for fabrication of electronic quantum devices. Here, we combine microtomy with vaporliquidsolid growth of III/V nanowires to create a scalable platform that can deterministically transfer large arrays of single and fused nanocrystals  offering single unit control and free choice of target substrate. We fabricate electronic devices on crosssectioned InAs nanowires with good yield and demonstrate their ability to exhibit quantum phenomena such as conductance quantization, single electron charging, and wave interference. Finally, we devise how the platform can host rationally designed semiconductor/superconductor networks relevant for emerging quantum technologies.
 2111.05098v1 [pdf]
Joachim E. Sestoft, Aske N. Gejl, Thomas Kanne, Rasmus D. Schlosser, Daniel Ross, Daniel Kjær, Kasper GroveRasmussen, Jesper Nygård [pdf]

Quasiperiodic FloquetThouless Energy Pump 
Abstract
 Recent work [M. H. Kolodrubetz et al, PRL 120, 150601] has demonstrated that periodically driven onedimensional fermionic systems can support quantized energy pumping resulting from an adiabatic modulation of a second parameter. In this work, we explore this topological FloquetThouless energy pump in the quasiperiodic driving regime where the parametric driving occurs at finite frequency. We show that quantization of energy pumping persists for finite ramping frequencies, as long as they are incommensurate with the driving frequency, and the system remains localized by spatial disorder. Thus, the topological FloquetThouless energy pump is stable beyond the adiabatic regime, occupying a finite region of parameter space. Phase transitions away from these topological phases are accompanied by delocalization in position space, photon number (energy) space, or both. Using a dimensional reduction scheme, we demonstrate that a related phase can be realized with a cavityqubit system driven by two incommensurate modes.
Frederik Nathan, Rongchun Ge, Snir Gazit, Mark S. Rudner, Michael Kolodrubetz Journal reference: Phys. Rev. Lett. 127, 166804 (2021) [pdf] DOI: 10.1103/PhysRevLett.127.166804

Simultaneous Operations in a TwoDimensional Array of SingletTriplet Qubits 
Abstract
 In many physical approaches to quantum computation, errorcorrection schemes assume the ability to form twodimensional qubit arrays with nearestneighbor couplings and parallel operations at multiple qubit sites. While semiconductor spin qubits exhibit long coherence times relative to their operation speed and singlequbit fidelities above error correction thresholds, multiqubit operations in twodimensional arrays have been limited by fabrication, operation, and readout challenges. We present a twobytwo array of four singlettriplet qubits in gallium arsenide and show simultaneous coherent operations and fourqubit measurements via exchange oscillations and frequencymultiplexed singleshot measurements. A larger multielectron quantum dot is fabricated in the center of the array as a tunable interqubit link, which we utilize to demonstrate coherent spin exchange with selected qubits. Our techniques are extensible to other materials, indicating a path towards quantum processors with gatecontrolled spin qubits.
Federico Fedele, Anasua Chatterjee, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Ferdinand Kuemmeth Journal reference: PRX Quantum 2, 040306 (2021) [pdf] DOI: 10.1103/PRXQuantum.2.040306

Readout of parafermionic states by transport measurements 
Abstract
 Recent experiments have demonstrated the possibility of inducing superconducting pairing into counterpropagating fractional quantum Hall edge modes. This paves the way for the realization of localized parafermionic modes, nonabelian anyons which share fractional charges in a nonlocal way. We show that, for a pair of isolated parafermions, this nonlocal degree of freedom can be read by conductance measurements across standard metallic electrodes. We investigate first the transport through a grounded superconductor hosting two interacting parafermions. In the lowenergy limit, the conductance reveals their shared fractional charge. We then examine the twoterminal electron conductance of a blockaded fractional topological superconductor. Depending on the induced pairing, parafermion overlap, and charging energy, such a device displays different patterns as a function of its induced charge. The zerobias conductance allows us to distinguish a stronglyblockaded quantum dot regime, an intermediate pairing regime with a sixfold pattern of peaks repeating with periodicity $2e$, and a deep topological regime characterized by an $e/3$ periodicity.
 2109.02300v1 [pdf]
Ida E. Nielsen, Karsten Flensberg, Reinhold Egger, Michele Burrello [pdf]

Demonstrating Majorana nonabelian exchange using fast adiabatic
chargetransfer 
Abstract
 Demonstration of Majorana nonabelian exchange properties is a major challenge in the field of topological superconductivity. In this work, we propose a minimal device and protocol for testing nonabelian exchange properties using chargetransfer operations between a quantum dot and two Majorana bound states combined with reading the parity state using a second dot. We use an adiabatic perturbation theory to find fast adiabatic paths to perform operations and to account for nonadiabatic errors. We find the ideal parameter sweep and a region in parameter space which reduces the chargetransfer operation time 12 orders of magnitude with respect to constant velocity driving. Using realistic parameters, we estimate that the lower bound for the time scale can be reduced to $\sim10$ ns. Deviations from the ideal parameters lead to the accumulation of an undesired dynamical phase, affecting the outcome of the proposed protocol. We furthermore suggest to reduce the influence from the dynamical phase using an angular echo.
 2107.11833v2 [pdf]
Svend Krøjer, Rubén Seoane Souto, Karsten Flensberg [pdf]

Autonomous estimation of highdimensional Coulomb diamonds from sparse
measurements 
Abstract
 Arrays of coupled quantum dots possess ground states governed by Coulomb energies, utilized prominently by singly occupied quantum dots that each implement a spin qubit. For such quantum processors, the controlled transitions between one ground state to another are of significant operational significance, as these allow movements of quantum information within the array (singleelectron shuttling and qubit initialization) or wave function overlap of one spin with another (entangling gates and teleportation). For fewdot arrays, the ground state regions (Coulomb diamonds) are traditionally mapped out by performing dense measurements in controlvoltage space. For larger dot arrays, such raster scans become impractical, due to the large number of measurements needed to sample the highdimensional gatevoltage hypercube, and the comparatively little information one extracts from such dense scans (boundaries of Coulomb diamonds). In this work, we use adaptive lowdimensional line searches proposed by a learning algorithm within a highdimensional voltage space and combine this with a hardware triggered detection method based on reflectometry, to acquire sparse measurements that directly correspond to transitions between different ground states within the array. Our autonomous softwarehardware algorithm terminates by accurately estimating the polytope of Coulomb blockade boundaries, which we experimentally demonstrate in a 2$\times$2 array of silicon quantum dots.
 2108.10656v1 [pdf]
Anasua Chatterjee, Fabio Ansaloni, Torbjørn Rasmussen, Bertram Brovang, Federico Fedele, Heorhii Bohuslavskyi, Oswin Krause, Ferdinand Kuemmeth [pdf]

Estimation of Convex Polytopes for Automatic Discovery of Charge State
Transitions in Quantum Dot Arrays 
Abstract
 In spin based quantum dot arrays, a leading technology for quantum computation applications, material or fabrication imprecisions affect the behaviour of the device, which is compensated via tuning parameters. Automatic tuning of these device parameters constitutes a formidable challenge for machinelearning. Here, we present the first practical algorithm for controlling the transition of electrons in a spin qubit array. We exploit a connection to computational geometry and phrase the task as estimating a convex polytope from measurements. Our proposed algorithm uses active learning, to find the count, shapes and sizes of all facets of a given polytope. We test our algorithm on artifical polytopes as well as a real 2x2 spin qubit array. Our results show that we can reliably find the facets of the polytope, including small facets with sizes on the order of the measurement precision. We discuss the implications of the NPhardness of the underlying estimation problem and outline design considerations, limitations and tuning strategies for controlling future largescale spin qubit devices.
 2108.09133v1 [pdf]
Oswin Krause, Torbjørn Rasmussen, Bertram Brovang, Anasua Chatterjee, Ferdinand Kuemmeth [pdf]

Dynamical vortices in electronphonon superconductors 
Abstract
 We analyze the structure of an $s$wave superconducting gap in systems with electronphonon attraction and electronelectron repulsion. Earlier works have found that superconductivity develops despite strong repulsion, but the gap, $\Delta (\omega_m)$, necessarily changes sign along the Matsubara axis. We analyze the signchanging gap function from a topological perspective using the knowledge that a nodal point of $\Delta (\omega_m)$ is the center of dynamical vortex. We consider two models with different cutoffs for the repulsive interaction and trace the vortex positions along the Matsubara axis and in the upper frequency half plane upon changing the relative strength of the attractive and repulsive parts of the interaction. We discuss how the presence of dynamical vortices affects the gap structure along the real axis, detectable in ARPES experiments.
Morten H. Christensen, Andrey V. Chubukov Journal reference: Phys. Rev. B 104, 140501 (2021) [pdf] DOI: 10.1103/PhysRevB.104.L140501

Multilevel effects in quantum dot based paritytocharge conversion of Majorana box qubits 
Abstract
 Quantumdot based paritytocharge conversion is a promising method for reading out quantum information encoded nonlocally into pairs of Majorana zero modes. To obtain a sizable paritytocharge visibility, it is crucial to tune the relative phase of the tunnel couplings between the dot and the Majorana modes appropriately. However, in the presence of multiple quasidegenerate dot orbitals, it is in general not experimentally feasible to tune all couplings individually. This paper shows that such configurations could make it difficult to avoid a destructive multiorbital interference effect that substantially reduces the readout visibility. We analyze this effect using a Lindblad quantum master equation. This exposes how the experimentally relevant system parameters enhance or suppress the visibility when strong charging energy, measurement dissipation and, most importantly, multiorbital interference is accounted for. In particular, we find that an intermediatetime readout could mitigate some of the interferencerelated visibility reductions affecting the stationary limit.
Jens Schulenborg, Michele Burrello, Martin Leijnse, Karsten Flensberg Journal reference: Phys. Rev. B 103, 245407 (2021) [pdf] DOI: 10.1103/PhysRevB.103.245407

Asymmetric Little–Parks oscillations in full shell double nanowires 
Abstract
 LittleParks oscillations of a hollow superconducting cylinder are of interest for fluxdriven topological superconductivity in single Rashba nanowires. The oscillations are typically symmetric in the orientation of the applied magnetic flux. Using double InAs nanowires coated by an epitaxial superconducting Al shell which, despite the noncentrosymmetric geometry, behaves effectively as one hollow cylinder, we demonstrate that a small misalignment of the applied parallel field with respect to the axis of the nanowires can produce fieldasymmetric LittleParks oscillations. These are revealed by the simultaneous application of a magnetic field perpendicular to the misaligned parallel field direction. The asymmetry occurs in both the destructive regime, in which superconductivity is destroyed for halfinteger quanta of flux through the shell, and in the nondestructive regime, where superconductivity is depressed but not fully destroyed at these flux values.
Alexandros Vekris, Juan Carlos Estrada Saldaña, Joeri de Bruijckere, Sara Lorić, Thomas Kanne, Mikelis Marnauza, Dags Olsteins, Jesper Nygård, Kasper GroveRasmussen Journal reference: Scientific Reports 11, 19034 (2021) [pdf] DOI: 10.1038/s41598021977809

Coulombic subgap states 
Abstract
 Energy gaps are ubiquitous in the solid state. While in superconductors the BardeenCooperSchrieffer gap comes from Cooper pairing mediated by the crystal lattice, in Mott insulators the Coulomb gap results instead from electronelectron interactions. These gaps can be populated by subgap states due to various mechanisms. Here we demonstrate the existence of \textit{Coulombic} states, a new type of subgap states arising in a device with an energy gap opened by both Cooper pairing and Coulomb repulsion. The hybrid gap is provided by a superconducting island in Coulomb blockade, while the states arise due to electron transfer between the island and a nearby quantum dot. The Coulomb interaction in the device produces an unusual excitation spectrum exhibiting broken electronhole energy symmetry, discontinuity of spectral curves, strongly renormalized gfactors and highdegeneracy points. The repercussions of the new states for the search of Majorana states in topological superconducting islands are elucidated.
 2101.10794v2 [pdf]
Juan Carlos Estrada Saldaña, Alexandros Vekris, Luka Pavešič, Peter Krogstrup, Rok Žitko, Kasper GroveRasmussen, Jesper Nygård [pdf]

Comparing tunneling spectroscopy and charge sensing of Andreev bound
states in a semiconductorsuperconductor hybrid nanowire structure 
Abstract
 Transport studies of Andreev bound states (ABSs) are complicated by the interplay of charging effects and superconductivity. Here, we compare transport approaches to ABS spectroscopy in a semiconductorsuperconductor island to a chargesensing approach based on an integrated radiofrequency singleelectron transistor. Consistency of the methods demonstrates that fast, noninvasive charge sensing allows accurate quantitative measurement of ABSs while eluding some complexities of transport.
 2105.08871v1 [pdf]
Deividas Sabonis, David van Zanten, Judith Suter, Torsten Karzig, Dmitry I. Pikulin, Jukka I. Väyrynen, Eoin O'Farrell, Davydas Razmadze, Peter Krogstrup, Charles M. Marcus [pdf]

Direct Transport between Superconducting Subgap States in a Double
Quantum Dot 
Abstract
 We demonstrate direct transport between two opposing sets of YuShibaRusinov (YSR) subgap states realized in a double quantum dot. This subgap transport relies on intrinsic quasiparticle relaxation, but the tunability of the device allows us to explore also an additional relaxation mechanism based on charge transferring Andreev reflections. The transition between these two relaxation regimes is identified in the experiment as a marked gateinduced stepwise change in conductance. We present a transport calculation, including YSR bound states and multiple Andreev reflections alongside with quasiparticle relaxation, due to a weak tunnel coupling to a nearby normal metal, and obtain excellent agreement with the data.
 2105.06815v1 [pdf]
Gorm Ole Steffensen, Juan Carlos Estrada Saldaña, Alexandros Vekris, Peter Krogstrup, Kasper GroveRasmussen, Jesper Nygård, Alfredo Levy Yeyati, Jens Paaske [pdf]

Josephson junctions in double nanowires bridged by

Abstract
 We characterize parallel double quantum dot Josephson junctions based on closelygrown double nanowires bridged by insitu deposited superconductors. The parallel double dot behavior occurs despite the closeness of the nanowires and the potential risk of nanowire clamping during growth. By tuning the charge filling and lead couplings, we map out the simplest parallel double quantum dot YuShibaRusinov phase diagram. Our quasiindependent twowire hybrids show promise for the realization of exotic topological phases.
Alexandros Vekris, Juan Carlos Estrada Saldaña, Thomas Kanne, Mikelis Marnauza, Dags Olsteins, Furong Fan, Xiaobo Li, Thor HvidOlsen, Xiaohui Qiu, Hongqi Xu, Jesper Nygård, Kasper GroveRasmussen Journal reference: Phys. Rev. Research 3, 033240 (2021) [pdf] DOI: 10.1103/PhysRevResearch.3.033240

Spinpolarized bound states in
semiconductorsuperconductorferromagnetic insulator islands 
Abstract
 We report Coulomb blockade transport studies of InAs nanowires grown with epitaxial superconducting Al and ferromagnetic insulator EuS on overlapping facets. By comparing experimental results to a theoretical model, we associate cotunneling features in evenodd bias spectra with spinpolarized Andreev levels, indicating that spin splitting exceeding the induced superconducting gap at zero applied magnetic field. Energies of the polarized subgap states can be tuned on either side of zero by electrostatic gates.
 2104.01463v1 [pdf]
S. Vaitiekėnas, R. Seoane Souto, Y. Liu, P. Krogstrup, K. Flensberg, M. Leijnse, C. M. Marcus [pdf]

Andreev interference in the surface accumulation layer of halfshell
InAsSb/Al hybrid nanowires 
Abstract
 Understanding the spatial distribution of charge carriers in IIIV nanowires proximity coupled to superconductors is important for the design and interpretation of experiments based on hybrid quantum devices. In this letter, the gatedependent surface accumulation layer of InAsSb/Al nanowires was studied by means of Andreev interference in a parallel magnetic field. Both uniform hybrid nanowires and devices featuring a short Josephson junction fabricated by shadow lithography, exhibited periodic modulation of the switching current. The period corresponds to a flux quantum through the nanowire diameter and is consistent with Andreev bound states occupying a cylindrical surface accumulation layer. The spatial distribution was tunable by a gate potential as expected from electrostatic models.
 2104.00723v1 [pdf]
Lukas Stampfer, Damon J. Carrad, Dags Olsteins, Christian E. N. Petersen, Sabbir A. Khan, Peter Krogstrup, Thomas S. Jespersen [pdf]

The role of growth temperature on the electron mobility of
InAs/In$_x$Ga$_{1x}$As selective area grown nanowires 
Abstract
 Semiconductor nanowire networks are essential elements for a variety of gatetunable quantum applications. Their relevance, however, depends critically on the material quality. In this work we study selective area growth (SAG) of highly latticemismatched InAs/In$_x$Ga$_{1x}$As nanowires on insulating GaAs(001) substrates and address two key challenges: crystalline quality and compositional uniformity. We introduce optimization steps and show how misfit dislocations are guided away from the InAs active region and how GaIn intermixing is kinetically limited with growth temperature. The optimization process leads to a more than twofold increase in electron mobility and shows an advancement toward realizing high quality gatable quantum wire networks.
 2103.15971v1 [pdf]

Prethermalization and entanglement dynamics in interacting topological
pumps 
Abstract
 We investigate the formation of quasisteady states in onedimensional pumps of interacting fermions at noninteger filling fraction, in the regime where the driving frequency and interaction strength are small compared to the instantaneous singleparticle band gap throughout the driving cycle. The system rapidly absorbs energy from the driving field, and approaches a quasisteady state that locally resembles a maximal entropy state subject to the constraint of fixed particle number in each of the system's singleparticle Floquet bands. We explore the nature of this quasisteady state through onebody observables including the pumped current and natural orbital occupations, as well as the (manybody) entanglement spectrum and entropy. Potential disorder significantly reduces the amplitude of fluctuations of the quasisteady state current around its universal value, while the lifetime of the quasisteady state remains nearly unaffected for disorder strengths up to the scale of the singleparticle band gap. Interestingly, the natural orbital occupations and entanglement entropy display patterns signifying the periodic entangling and disentangling of the system's degrees of freedom over each driving cycle. Moreover, prominent features in the system's timedependent entanglement spectrum reveal the emergence of new long timescales associated with the equilibration of manyparticle correlations.
 2103.15831v1 [pdf]
Raffael Gawatz, Ajit C. Balram, Erez Berg, Netanel H. Lindner, Mark S. Rudner [pdf]

Threephase Majorana zero modes at tiny magnetic fields 
Abstract
 Proposals for realizing Majorana fermions in condensed matter systems typically rely on magnetic fields, which degrade the proximitizing superconductor and plague the Majoranas' detection. We propose an alternative scheme to realize Majoranas based only on phasebiased superconductors. The phases (at least three of them) can be biased by a tiny magnetic field threading macroscopic superconducting loops, focusing and enhancing the effect of the magnetic field onto the junction, or by supercurrents. We show how a combination of the superconducting phase winding and the spinorbit phase induced in closed loops (AharonovCasher effect) facilitates a topological superconducting state with Majorana end states. We demontrate this scheme by an analytically tractable model as well as simulations of realistic setups comprising only conventional materials.
Omri Lesser, Karsten Flensberg, Felix von Oppen, Yuval Oreg Journal reference: Phys. Rev. B 103, 121116 (2021) [pdf] DOI: 10.1103/PhysRevB.103.L121116

Double nanowires for hybrid quantum devices 
Abstract
 Parallel onedimensional semiconductor channels connected by a superconducting strip constitute the core platform in several recent quantum device proposals that rely e.g. on Andreev processes or topological effects. In order to realize these proposals, the actual material systems must have high crystalline purity and the coupling between the different elements should be controllable in terms of their interfaces and geometry. We present a strategy for synthesizing double InAs nanowires by the vaporliquidsolid mechanism using IIIV molecular beam epitaxy. A superconducting layer is deposited onto nanowires without breaking vacuum, ensuring pristine interfaces between the superconductor and the two semiconductor nanowires. The method allows for a high yield of merged as well as separate parallel nanowires, with full or halfshell superconductor coatings. We demonstrate their utility in complex quantum devices by electron transport measurements.
 2103.13938v1 [pdf]

Topological superconductivity in semiconductor–superconductor–magneticinsulator heterostructures 
Abstract
 Hybrid superconductorsemiconductor heterostructures are promising platforms for realizing topological superconductors and exploring Majorana bound states physics. Motivated by recent experimental progress, we theoretically study how magnetic insulators offer an alternative to the use of external magnetic fields for reaching the topological regime. We consider different setups, where: (1) the magnetic insulator induces an exchange field in the superconductor, which leads to a splitting in the semiconductor by proximity effect, and (2) the magnetic insulator acts as a spinfilter tunnel barrier between the superconductor and the semiconductor. We show that the spin splitting in the superconductor alone cannot induce a topological transition in the semiconductor. To overcome this limitation, we propose to use a spinfilter barrier that enhances the magnetic exchange and provides a mechanism for a topological phase transition. Moreover, the spindependent tunneling introduces a strong dependence on the band alignment, which can be crucial in quantumconfined systems. This mechanism opens up a route towards networks of topological wires with fewer constraints on device geometry compared to previous devices that require external magnetic fields.
A. Maiani, R. Seoane Souto, M. Leijnse, K. Flensberg Journal reference: Phys. Rev. B 103, 104508 (2021) [pdf] DOI: 10.1103/PhysRevB.103.104508

Engineered platforms for topological superconductivity and Majorana zero
modes 
Abstract
 Among the major approaches that are being pursued for realizing quantum bits, the Majoranabased platform has been the most recent to be launched. It attempts to realize qubits which store quantum information in a topologicallyprotected manner. The quantum information is protected by its nonlocal storage in localized and wellseparated Majorana zero modes, and manipulated by exploiting their nonabelian quantum exchange properties. Realizing these topological qubits is experimentally challenging, requiring superconductivity, helical electrons (created by spinorbit coupling) and breaking of time reversal symmetry to all cooperate in an uncomfortable alliance. Over the past decade, several candidate material systems for realizing Majoranabased topological qubits have been explored, and there is accumulating, though still debated, evidence that zero modes are indeed being realized. This paper reviews the basic physical principles on which these approaches are based, the material systems that are being developed, and the current state of the field. We highlight both the progress made and the challenges that still need to be overcome.
 2103.05548v1 [pdf]
Karsten Flensberg, Felix von Oppen, Ady Stern [pdf]


Abstract
 Under the perspective of realizing analog quantum simulations of lattice gauge theories, ladder geometries offer an intriguing playground, relevant for ultracold atom experiments. Here, we investigate Hamiltonian lattice gauge theories defined in twoleg ladders. We consider a model that includes both gauge boson and Higgs matter degrees of freedom with local $\mathbb{Z}_N$ gauge symmetries. We study its phase diagram based on both an effective lowenergy field theory and density matrix renormalization group simulations. For $N\ge 5$, an extended gapless Coulomb phase emerges, which is separated by a BerezinskiiKosterlitzThouless phase transition from the surrounding gapped phase. Besides the traditional confined and Higgs regimes, we also observe a novel quadrupolar region, originated by the ladder geometry.
Jens Nyhegn, ChiaMin Chung, Michele Burrello Journal reference: Phys. Rev. Research 3, 013133 (2021) [pdf] DOI: 10.1103/PhysRevResearch.3.013133

Zeemandriven parity transitions in an Andreev quantum dot 
Abstract
 The Andreev spectrum of a quantum dot embedded in a hybrid semiconductorsuperconductor interferometer can be modulated by electrostatic gating, magnetic flux through the interferometer, and Zeeman splitting from inplane magnetic field. We demonstrate parity transitions in the embedded quantum dot system, and show that the Zeemandriven transition is accompanied by a 0{\pi} transition in the superconducting phase across the dot. We further demonstrate that flux through the interferometer modulates both dot parity and 0{\pi} transitions.
A. M. Whiticar, A. Fornieri, A. Banerjee, A. C. C. Drachmann, S. Gronin, G. C. Gardner, T. Lindemann, M. J. Manfra, C. M. Marcus Journal reference: Phys. Rev. B 103, 245308 (2021) [pdf] DOI: 10.1103/PhysRevB.103.245308

Roadmap on quantum nanotechnologies 
Abstract
 Quantum phenomena are typically observable at length and time scales smaller than those of our everyday experience, often involving individual particles or excitations. The past few decades have seen a revolution in the ability to structure matter at the nanoscale, and experiments at the single particle level have become commonplace. This has opened wide new avenues for exploring and harnessing quantum mechanical effects in condensed matter. These quantum phenomena, in turn, have the potential to revolutionize the way we communicate, compute and probe the nanoscale world. Here, we review developments in key areas of quantum research in light of the nanotechnologies that enable them, with a view to what the future holds. Materials and devices with nanoscale features are used for quantum metrology and sensing, as building blocks for quantum computing, and as sources and detectors for quantum communication. They enable explorations of quantum behaviour and unconventional states in nano and optomechanical systems, lowdimensional systems, molecular devices, nanoplasmonics, quantum electrodynamics, scanning tunnelling microscopy, and more. This rapidly expanding intersection of nanotechnology and quantum science/technology is mutually beneficial to both fields, laying claim to some of the most exciting scientific leaps of the last decade, with more on the horizon.
Arne Laucht, Frank Hohls, Niels Ubbelohde, M Fernando GonzalezZalba, David J Reilly, Søren Stobbe, Tim Schröder, Pasquale Scarlino, Jonne V Koski, Andrew Dzurak, ChihHwan Yang, Jun Yoneda, Ferdinand Kuemmeth, Hendrik Bluhm, Jarryd Pla, Charles Hill, Joe Salfi, Akira Oiwa, Juha T Muhonen, Ewold Verhagen, Matthew D LaHaye, Hyun Ho Kim, Adam W Tsen, Dimitrie Culcer, Attila Geresdi, Jan A Mol, Varun Mohan, Prashant K Jain, Jonathan Baugh Journal reference: Nanotechnology 32, 162003 (2021) [pdf] DOI: 10.1088/13616528/abb333

MagneticFieldCompatible Superconducting Transmon Qubit 
Abstract
 We present a hybrid semiconductorbased superconducting qubit device which remains coherent at magnetic fields up to 1 T. The qubit transition frequency exhibits periodic oscillations with magnetic field, consistent with interference effects due to the magnetic flux threading the cross section of the proximitized semiconductor nanowire junction. As induced superconductivity revives, additional coherent modes emerge at high magnetic fields, which we attribute to the interaction of the qubit and lowenergy Andreev states.
A. Kringhøj, T. W. Larsen, O. Erlandsson, W. Uilhoorn, J. G. Kroll, M. Hesselberg, R. P. G. McNeil, P. Krogstrup, L. Casparis, C. M. Marcus, K. D. Petersson Journal reference: Phys. Rev. Applied 15, 054001 (2021) [pdf] DOI: 10.1103/PhysRevApplied.15.054001

Anodic oxidation of epitaxial superconductorsemiconductor hybrids 
Abstract
 We demonstrate a new fabrication process for hybrid semiconductorsuperconductor heterostructures based on anodic oxidation (AO), allowing controlled thinning of epitaxial Al films. Structural and transport studies of oxidized epitaxial Al films grown on insulating GaAs substrates reveal spatial nonuniformity and enhanced critical temperature and magnetic fields. Oxidation of epitaxial Al on hybrid InAs heterostructures with a conducting quantum well show similarly enhanced superconducting properties transferred to the twodimensional electron gas (2DEG) by proximity effect, with critical perpendicular magnetic fields up to 3.5 T. An insulating AlOx film, that passivates the heterostructure from exposure to air, is obtained by complete oxidation of the Al. It simultaneously removes the need to strip Al which damages the underlying semiconductor. AO passivation yielded 2DEG mobilities two times higher than similar devices with Al removed by wet etching. An AOpassivated Hall bar showed quantum Hall features emerging at a transverse field of 2.5 T, below the critical transverse field of thinned films, eventually allowing transparent coupling of quantum Hall effect and superconductivity. AO thinning and passivation are compatible with standard lithographic techniques, giving lateral resolution below <50 nm. We demonstrate local patterning of AO by realizing a semiconductorbased Josephson junction operating up to 0.3 T perpendicular.
Asbjørn C. C. Drachmann, Rosa E. Diaz, Candice Thomas, Henri J. Suominen, Alexander M. Whiticar, Antonio Fornieri, Sergei Gronin, Tiantian Wang, Geoffrey C. Gardner, Alex R. Hamilton, Fabrizio Nichele, Michael J. Manfra, Charles M. Marcus Journal reference: Phys. Rev. Materials 5, 013805 (2021) [pdf] DOI: 10.1103/PhysRevMaterials.5.013805

Andreev Modes from Phase Winding in a FullShell NanowireBased Transmon 
Abstract
 We investigate transmon qubits made from semiconductor nanowires with a fully surrounding superconducting shell. In the regime of reentrant superconductivity associated with the destructive LittleParks effect, numerous coherent transitions are observed in the first reentrant lobe, where the shell carries 2{\pi} winding of superconducting phase, and are absent in the zeroth lobe. As junction density was increased by gate voltage, qubit coherence was suppressed then lost in the first lobe. These observations and numerical simulations highlight the role of windinginduced Andreev states in the junction.
A. Kringhøj, G. W. Winkler, T. W. Larsen, D. Sabonis, O. Erlandsson, P. Krogstrup, B. van Heck, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. Lett. 126, 047701 (2021) [pdf] DOI: 10.1103/PhysRevLett.126.047701

Spatially dispersing YuShibaRusinov states in the unconventional superconductor FeTe0.55Se0.45 
Abstract
 By using scanning tunneling microscopy (STM) we find and characterize dispersive, energysymmetric ingap states in the ironbased superconductor $\mathrm{FeTe}_{0.55}\mathrm{Se}_{0.45}$, a material that exhibits signatures of topological superconductivity, and Majorana bound states at vortex cores or at impurity locations. We use a superconducting STM tip for enhanced energy resolution, which enables us to show that impurity states can be tuned through the Fermi level with varying tipsample distance. We find that the impurity state is of the YuShibaRusinov (YSR) type, and argue that the energy shift is caused by the low superfluid density in $\mathrm{FeTe}_{0.55}\mathrm{Se}_{0.45}$, which allows the electric field of the tip to slightly penetrate the sample. We model the newly introduced tipgating scenario within the singleimpurity Anderson model and find good agreement to the experimental data.
Damianos Chatzopoulos, Doohee Cho, Koen M. Bastiaans, Gorm O. Steffensen, Damian Bouwmeester, Alireza Akbari, Genda Gu, Jens Paaske, Brian M. Andersen, Milan P. Allan Journal reference: Nature Communications 12, 298 (2021) [pdf] DOI: 10.1038/s4146702020529x

Closing of the induced gap in a hybrid superconductorsemiconductor nanowire 
Abstract
 Hybrid superconductorsemiconductor nanowires are predicted to undergo a fieldinduced phase transition from a trivial to a topological superconductor, marked by the closure and reopening of the excitation gap, followed by the emergence of Majorana bound states at the nanowire ends. Many local densityofstates measurements have reported signatures of the topological phase, however this interpretation has been challenged by alternative explanations. Here, by measuring nonlocal conductance, we identify the closure of the excitation gap in the bulk of the semiconductor before the emergence of zerobias peaks. This observation is inconsistent with scenarios where zerobias peaks occur due to endstates with a trivially gapped bulk, which have been extensively considered in the theoretical and experimental literature. We observe that after the gap closes, nonlocal signals fluctuate strongly and persist irrespective of the presence of localconductance zerobias peaks. Thus, our observations are also incompatible with a simple picture of clean topological superconductivity. This work presents a new experimental approach for probing the spatial extent of states in Majorana wires, and reveals the presence of a regime with a continuum of spatially extended states and uncorrelated zerobias peaks.
D. Puglia, E. A. Martinez, G. C. Ménard, A. Pöschl, S. Gronin, G. C. Gardner, R. Kallaher, M. J. Manfra, C. M. Marcus, A. P. Higginbotham, L. Casparis Journal reference: Phys. Rev. B 103, 235201 (2021) [pdf] DOI: 10.1103/PhysRevB.103.235201

Semiconductor qubits in practice 
Abstract
 In recent years semiconducting qubits have undergone a remarkable evolution, making great strides in overcoming decoherence as well as in prospects for scalability, and have become one of the leading contenders for the development of largescale quantum circuits. In this Review we describe the current state of the art in semiconductor charge and spin qubits based on gatecontrolled semiconductor quantum dots, shallow dopants, and color centers in wide band gap materials. We frame the relative strengths of the different semiconductor qubit implementations in the context of quantum simulations, computing, sensing and networks. By highlighting the status and future perspectives of the basic types of semiconductor qubits, this Review aims to serve as a technical introduction for nonspecialists as well as a forwardlooking reference for scientists intending to work in this field.
Anasua Chatterjee, Paul Stevenson, Silvano De Franceschi, Andrea Morello, Nathalie de Leon, Ferdinand Kuemmeth Journal reference: Nature Reviews Physics (2021) [pdf] DOI: 10.1038/s42254021002839

Epitaxial Pb on InAs nanowires for quantum devices 
Abstract
 Semiconductorsuperconductor hybrids are widely used for realising complex quantum phenomena such as topological superconductivity and spins coupled to Cooper pairs. Accessing exotic regimes at high magnetic fields and increasing operating temperatures beyond the stateoftheart requires new, epitaxially matched semiconductorsuperconductor materials. The challenge is to generate favourable conditions for heterostructure formation between materials with the desired inherent properties. Here, we harness increased knowledge of metalonsemiconductor growth to develop InAs nanowires with epitaxially matched, single crystal, atomically flat Pb films along the entire nanowire. These highly ordered heterostructures have a critical temperature of 7 K and a superconducting gap of 1.25 meV, which remains hard at 8.5 T, thereby more than doubling the available parameter space. Additionally, InAs/Pb island devics exhibit magnetic fielddriven transitions from Cooper pair to single electron charging; a prerequisite for use in topological quantum computation. Introducing semiconductorPb hybrids potentially enables access to entirely new regimes for an array of quantum systems.
Thomas Kanne, Mikelis Marnauza, Dags Olsteins, Damon J. Carrad, Joachim E. Sestoft, Joeri de Bruijckere, Lunjie Zeng, Erik Johnson, Eva Olsson, Kasper GroveRasmussen, Jesper Nygård Journal reference: Nature Nanotechnology (2021) [pdf] DOI: 10.1038/s41565021009009

Topological van Hove singularities at phase transitions in Weyl metals 
Abstract
 2020

Exploring helical phases of matter in bosonic ladders 
Abstract
 Ladder models of ultracold atoms offer a versatile platform for the experimental and theoretical study of different phenomena and phases of matter linked to the interplay between artificial gauge fields and interactions. Strongly correlated helical states are known to appear for specific ratios of the particle and magnetic flux densities and they can often be interpreted as a onedimensional limit of fractional quantum Hall states, thus being called pretopological. Their signatures, however, are typically hard to observe due to the small gaps characterizing these states. Here we investigate bosonic ladder models at filling factor 1. Based on bosonization, renormalization group and matrix product state simulations we pinpoint two strongly correlated helical phases appearing at this resonance. We show that one of them can be accessed in systems with twospecies hardcore bosons and onsite repulsions only, thus amenable for optical lattice experiments. Its signatures are sizable and stable over a broad range of parameters for realistic system sizes.
Andreas Haller, Apollonas S. MatsoukasRoubeas, Yueting Pan, Matteo Rizzi, Michele Burrello Journal reference: Phys. Rev. Research 2, 043433 (2020) [pdf] DOI: 10.1103/PhysRevResearch.2.043433

Reflectometry of charge transitions in a silicon quadruple dot 
Abstract
 Gatecontrolled silicon quantum devices are currently moving from academic proofofprinciple studies to industrial fabrication, while increasing their complexity from single or doubledot devices to larger arrays. We perform gatebased highfrequency reflectometry measurements on a 2x2 array of silicon quantum dots fabricated entirely using 300 mm foundry processes. Utilizing the capacitive couplings within the dot array, it is sufficient to connect only one gate electrode to one reflectometry resonator and still establish singleelectron occupation in each of the four dots and detect singleelectron movements with high bandwidth. A global topgate electrode adjusts the overall tunneling times, while linear combinations of sidegate voltages yield detailed charge stability diagrams. We support our findings with $\mathbf{k}\cdot\mathbf{p}$ modeling and electrostatic simulations based on a constant interaction model, and experimentally demonstrate singleshot detection of interdot charge transitions with unity signaltonoise ratios at bandwidths exceeding 30 kHz. Our techniques may find use in the scaling of fewdot spinqubit devices to largescale quantum processors.
 2012.04791v1 [pdf]

Roadmap for gallium arsenide spin qubits 
Abstract
 Gatedefined quantum dots in gallium arsenide (GaAs) have been used extensively for pioneering spin qubit devices due to the relative simplicity of fabrication and favourable electronic properties such as a single conduction band valley, a small effective mass, and stable dopants. GaAs spin qubits are readily produced in many labs and are currently studied for various applications, including entanglement, quantum nondemolition measurements, automatic tuning, multidot arrays, coherent exchange coupling, and teleportation. Even while much attention is shifting to other materials, GaAs devices will likely remain a workhorse for proofofconcept quantum information processing and solidstate experiments.
 2011.13907v1 [pdf]
Ferdinand Kuemmeth, Hendrik Bluhm [pdf]

Response to "Comment on Universal Lindblad Equation for open quantum
systems" 
Abstract
 In a recent comment, Lee and Yeo show that the Gibbs state is not generically an exact steady state of the Universal Lindblad Equation (ULE) that we developed in Phys. Rev. B 102, 115109 (2020). This noncontroversial observation is precisely as expected for open quantum systems with finite systembath coupling, where transition rates may be comparable to or larger than the level spacing of the system, and we made no claim to the contrary in our paper. The comment by Lee and Yeo hence highlights that the ULE captures contributions to the steady state due to finite systembath coupling that are beyond the reach of master equations that rely on rotating wave approximations. In this response we further clarify the nature of our analytical and numerical results.
 2011.04574v1 [pdf]
Frederik Nathan, Mark S. Rudner [pdf]

Twoimpurity YuShibaRusinov states in coupled quantum dots 
Abstract
 Using double quantum dots as the weak link of a Josephson junction, we realize the superconducting analog of the celebrated twoimpurity Kondo model. The device shows a cusped currentvoltage characteristic, which can be modelled by an overdamped circuit relating the observed cusp current to the Josephson critical current. The gate dependence of the cusp current and of the subgap spectra are used as complementary groundstate indicators to demonstrate gatetuned changes of the ground state from an interdot singlet to independently screened YuShibaRusinov (YSR) singlets. In contrast to the twoimpurity Kondo effect in normalstate systems, the crossover between these two singlets is heralded by quantum phase boundaries to nearby doublet YSR phases in which only a single spin is screened.
J. C. Estrada Saldaña, A. Vekris, R. Žitko, G. Steffensen, P. Krogstrup, J. Paaske, K. GroveRasmussen, J. Nygård Journal reference: Physical Review B 102, 195143 (2020) [pdf] DOI: 10.1103/PhysRevB.102.195143

Universal Lindblad equation for open quantum systems 
Abstract
 We develop a Markovian master equation in the Lindblad form that enables the efficient study of a wide range of open quantum manybody systems that would be inaccessible with existing methods. The validity of the master equation is based entirely on properties of the bath and the systembath coupling, without any requirements on the level structure within the system itself. The master equation is derived using a Markov approximation that is distinct from that used in earlier approaches. We provide a rigorous bound for the error induced by this Markov approximation; the error is controlled by a dimensionless combination of intrinsic correlation and relaxation timescales of the bath. Our master equation is accurate on the same level of approximation as the BlochRedfield equation. In contrast to the BlochRedfield approach, our approach ensures preservation of the positivity of the density matrix. As a result, our method is robust, and can be solved efficiently using stochastic evolution of pure states (rather than density matrices). We discuss how our method can be applied to static or driven quantum manybody systems, and illustrate its power through numerical simulation of a spin chain that would be challenging to treat by existing methods.
Frederik Nathan, Mark S. Rudner Journal reference: Phys. Rev. B 102, 115109 (2020) [pdf] DOI: 10.1103/PhysRevB.102.115109

ParityProtected SuperconductorSemiconductor Qubit 
Abstract
 Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parityprotected qubit based on voltagecontrolled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energyphase relation of fewchannel junctions. A symmetric interferometer formed by two such junctions, gatetuned into balance and frustrated by a halfquantum of applied flux, yields a cos(2{\phi}) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate that relaxation of the qubit can be suppressed tenfold by tuning into the protected regime.
T. W. Larsen, M. E. Gershenson, L. Casparis, A. Kringhøj, N. J. Pearson, R. P. G. McNeil, F. Kuemmeth, P. Krogstrup, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. Lett. 125, 056801 (2020) [pdf] DOI: 10.1103/PhysRevLett.125.056801

Contrasting lattice geometry dependent versus independent quantities: Ramifications for Berry curvature, energy gaps, and dynamics 
Abstract
 In the tightbinding description of electronic, photonic, or cold atomic dynamics in a periodic lattice potential, particle motion is described in terms of hopping amplitudes and potentials on an abstract network of discrete sites corresponding to physical orbitals in the lattice. The physical attributes of the orbitals, including their locations in threedimensional space, are independent pieces of information. In this paper we identify a notion of geometryindependence: any physical quantity or observable that depends only on the tightbinding parameters (and not on the explicit information about the orbital geometry) is said to be "geometryindependent." The band structure itself, and for example the Chern numbers of the bands in a twodimensional system, are geometryindependent, while the Blochband Berry curvature is geometrydependent. Careful identification of geometrydependent versus independent quantities can be used as a novel principle for constraining a variety of results. By extending the notion of geometryindependence to certain classes of interacting systems, where the manybody energy gap is evidently geometryindependent, we shed new light on a hypothesized relation between manybody energy gaps of fractional Chern insulators and the uniformity of Bloch band Berry curvature in the Brillouin zone. We furthermore explore the geometrydependence of semiclassical wave packet dynamics, and use this principle to show how two different types of Hall response measurements may give markedly different results due to the fact that one is geometrydependent, while the other is geometryindependent. Similar considerations apply for anomalous thermal Hall response, in both electronic and spin systems.
Steven H. Simon, Mark S. Rudner Journal reference: Phys. Rev. B 102, 165148 (2020) [pdf] DOI: 10.1103/PhysRevB.102.165148

Longdistance coherence of Majorana wires 
Abstract
 Theoretically, a pair of Majorana bound states in a topological superconductor forms a single fermionic level even at large separations, implying that the parity information is stored nonlocally. The nonlocality leads to a longdistance coherence for electrons tunneling through a Coulomb blockaded Majorana wire [Fu, Phys. Rev. Lett. 104, 056402 (2010)], an effect that can be observed, e.g., in an interferometer. Here, we examine theoretically the coherent electron transfer, taking into account that tunneling implies the longdistance transfer of charge, which is carried by onedimensional plasmons. We show that the charge dynamics does not affect the coherence of the electron tunneling process in a topological superconductor consisting of a semiconductor wire proximitized by a single bulk superconductor. The coherence may be strongly suppressed, however, if the topological superconductivity derives from a semiconductor wire proximitized by a granular superconductor.
Zheng Shi, Piet W. Brouwer, Karsten Flensberg, Leonid I. Glazman, Felix von Oppen Journal reference: Phys. Rev. B 101, 241414 (2020) [pdf] DOI: 10.1103/PhysRevB.101.241414

Coherent transport through a Majorana island in an Aharonov–Bohm interferometer 
Abstract
 Majorana zero modes are leading candidates for topological quantum computation due to nonlocal qubit encoding and nonabelian exchange statistics. Spatially separated Majorana modes are expected to allow phasecoherent singleelectron transport through a topological superconducting island via a mechanism referred to as teleportation. Here we experimentally investigate such a system by patterning an elongated epitaxial InAsAl island embedded in an AharonovBohm interferometer. With increasing parallel magnetic field, a discrete subgap state in the island is lowered to zero energy yielding persistent 1eperiodic Coulomb blockade conductance peaks (e is the elementary charge). In this condition, conductance through the interferometer is observed to oscillate in a perpendicular magnetic field with a flux period of h/e (h is Planck's constant), indicating coherent transport of single electrons through the islands, a signature of electron teleportation via Majorana modes, could also be observed, suggesting additional nonMajorana mechanisms for 1e transport through these moderately short wires.
A. M. Whiticar, A. Fornieri, E. C. T. O'Farrell, A. C. C. Drachmann, T. Wang, C. Thomas, S. Gronin, R. Kallaher, G. C. Gardner, M. J. Manfra, C. M. Marcus, F. Nichele Journal reference: Nat. Comm. 11, 3212 (2020) [pdf] DOI: 10.1038/s4146702016988x

The Floquet Engineer's Handbook 
Abstract
 We provide a pedagogical technical guide to many of the key theoretical tools and ideas that underlie work in the field of Floquet engineering. We hope that this document will serve as a useful resource for new researchers aiming to enter the field, as well as experienced researchers who wish to gain new insight into familiar or possibly unfamiliar methods. This guide was developed out of supplementary material as a companion to our recent review, "Band structure engineering and nonequilibrium dynamics in Floquet topological insulators," Nature Reviews Physics 2, 229 (2020). The primary focus is on analytical techniques relevant for FloquetBloch band engineering and related manybody dynamics. We will continue to update this document over time to include additional content, and welcome suggestions for further topics to consider.
 2003.08252v2 [pdf]
Mark S. Rudner, Netanel H. Lindner [pdf]

Reaching the quantum Hall regime with rotating Rydbergdressed atoms 
Abstract
 Despite the striking progress in the field of quantum gases, one of their much anticipated application  the simulation of quantum Hall states  remains elusive: all experimental approaches so far failed in reaching a sufficiently small ratio between atom and vortex densities. In this paper we consider rotating Rydbergdressed atoms in magnetic traps: these gases offer strong and tunable nonlocal repulsive interactions and very low densities; hence they provide an exceptional platform to reach the quantum Hall regime. Based on the Lindemann criterion and the analysis of the interplay of the length scales of the system, we show that there exists an optimal value of the dressing parameters that minimizes the ratio between the filling factor of the system and its critical value to enter the Hall regime, thus making it possible to reach this stronglycorrelated phase for more than 1000 atoms under realistic conditions.
Michele Burrello, Igor Lesanovsky, Andrea Trombettoni Journal reference: Phys. Rev. Research 2, 023290 (2020) [pdf] DOI: 10.1103/PhysRevResearch.2.023290

Quantum Dot Parity Effects in Trivial and Topological Josephson Junctions 
Abstract
 An oddoccupied quantum dot in a Josephson junction can flip transmission phase, creating a {\pi}junction. When the junction couples topological superconductors, no phase flip is expected. We investigate this and related effects in a fullshell hybrid interferometer, using gate voltage to control dotjunction parity and axial magnetic flux to control the transition from trivial to topological superconductivity. Enhanced zerobias conductance and critical current for odd parity in the topological phase reflects hybridization of the confined spin with zeroenergy modes in the leads.
D. Razmadze, E. C. T. O'Farrell, P. Krogstrup, C. M. Marcus Journal reference: Phys. Rev. Lett. 125, 116803 (2020) [pdf] DOI: 10.1103/PhysRevLett.125.116803

Shadow Epitaxy for In Situ Growth of Generic Semiconductor/Superconductor Hybrids 
Abstract
 Uniform, defectfree crystal interfaces and surfaces are crucial ingredients for realizing highperformance nanoscale devices. A pertinent example is that advances in gatetunable and topological superconductivity using semiconductor/superconductor electronic devices are currently built on the hard proximityinduced superconducting gap obtained from epitaxial indium arsenide/aluminium heterostructures. Fabrication of devices requires selective etch processes; these exist only for InAs/Al hybrids, precluding the use of other, potentially superior material combinations. We present a crystal growth platform  based on threedimensional structuring of growth substrates  which enables synthesis of semiconductor nanowire hybrids with insitu patterned superconductor shells. This platform eliminates the need for etching, thereby enabling full freedom in choice of hybrid constituents. We realise and characterise all the most frequently used architectures in superconducting hybrid devices, finding increased yield and electrostatic stability compared to etched devices, along with evidence of ballistic superconductivity. In addition to aluminium, we present hybrid devices based on tantalum, niobium and vanadium. This is the submitted version of the manuscript. The accepted, peer reviewed version is available from Advanced Materials: http://doi.org/10.1002/adma.201908411 Previous title: Shadow lithography for insitu growth of generic semiconductor/superconductor devices
Damon J. Carrad, Martin Bjergfelt, Thomas Kanne, Martin Aagesen, Filip Krizek, Elisabetta M. Fiordaliso, Erik Johnson, Jesper Nygård, Thomas Sand Jespersen Journal reference: Advanced Materials (2020) 1908411 [pdf] DOI: 10.1002/adma.201908411

Destructive LittleParks Effect in a FullShell NanowireBased Transmon 
Abstract
 A semiconductor transmon with an epitaxial Al shell fully surrounding an InAs nanowire core is investigated in the low $E_J/E_C$ regime. LittleParks oscillations as a function of flux along the hybrid wire axis are destructive, creating lobes of reentrant superconductivity separated by a metallic state at a halfquantum of applied flux. In the first lobe, phase winding around the shell can induce topological superconductivity in the core. Coherent qubit operation is observed in both the zeroth and first lobes. Splitting of parity bands by coherent singleelectron coupling across the junction is not resolved beyond line broadening, placing a bound on Majorana coupling, $E_M/h$ < 10 MHz, much smaller than the Josephson coupling $E_J/h$ ~ 4.7 GHz.
Deividas Sabonis, Oscar Erlandsson, Anders Kringhøj, Bernard van Heck, Thorvald W. Larsen, Ivana Petkovic, Peter Krogstrup, Karl D. Petersson, Charles M. Marcus Journal reference: Phys. Rev. Lett. 125, 156804 (2020) [pdf] DOI: 10.1103/PhysRevLett.125.156804

Paritytocharge conversion in Majorana qubit readout 
Abstract
 We study the timedependent effect of Markovian readout processes on Majorana qubits whose parity degrees of freedom are converted into the charge of a tunnelcoupled quantum dot. By applying a recently established effective Lindbladian approximation [13], we obtain a completely positive and trace preserving Lindblad master equation for the combined dotqubit dynamics, describing relaxation and decoherence processes beyond the rotatingwave approximation. This approach is applicable to a wide range of weakly coupled environments representing experimentally relevant readout devices. We study in detail the case of thermal decay in the presence of a generic Ohmic bosonic bath, in particular for potential fluctuations in an electromagnetic circuit. In addition, we consider the nonequilibrium measurement environment for a parity readout using a quantum point contact capacitively coupled to the dot charge.
Morten I. K. Munk, Jens Schulenborg, Reinhold Egger, Karsten Flensberg Journal reference: Phys. Rev. Research 2, 033254 (2020) [pdf] DOI: 10.1103/PhysRevResearch.2.033254

Zerobias peaks at zero magnetic field in ferromagnetic hybrid nanowires 
Abstract
 We report transport measurements and tunneling spectroscopy in hybrid nanowires with epitaxial layers of superconducting Al and the ferromagnetic insulator EuS, grown on semiconducting InAs nanowires. In devices where the Al and EuS covered facets overlap, we infer a remanent effective Zeeman field of order 1 T, and observe stable zerobias conductance peaks in tunneling spectroscopy into the end of the nanowire, consistent with topological superconductivity at zero applied field. Hysteretic features in critical current and tunneling spectra as a function of applied magnetic field support this picture. Nanowires with nonoverlapping Al and EuS covered facets do not show comparable features. Topological superconductivity in zero applied field allows new device geometries and types of control.
S. Vaitiekėnas, Y. Liu, P. Krogstrup, C. M. Marcus [pdf] DOI: 10.1038/s4156702010173 2004.02226v1 [pdf]

Singleelectron operations in a foundryfabricated array of quantum dots 
Abstract
 Silicon spin qubits have achieved highfidelity one and twoqubit gates, above error correction thresholds, promising an industrial route to faulttolerant quantum computation. A significant next step for the development of scalable multiqubit processors is the operation of foundryfabricated, extendable twodimensional (2D) arrays. In gallium arsenide, 2D quantumdot arrays recently allowed coherent spin operations and quantum simulations. In silicon, 2D arrays have been limited to transport measurements in the manyelectron regime. Here, we operate a foundryfabricated silicon 2x2 array in the fewelectron regime, achieving singleelectron occupation in each of the four gatedefined quantum dots, as well as reconfigurable single, double, and triple dots with tunable tunnel couplings. Pulsedgate and gatereflectometry techniques permit singleelectron manipulation and singleshot charge readout, while the twodimensionality allows the spatial exchange of electron pairs. The compact form factor of such arrays, whose foundry fabrication can be extended to larger 2xN arrays, along with the recent demonstration of coherent spin control and readout, paves the way for dense qubit arrays for quantum computation and simulation.
Fabio Ansaloni, Anasua Chatterjee, Heorhii Bohuslavskyi, Benoit Bertrand, Louis Hutin, Maud Vinet, Ferdinand Kuemmeth Journal reference: Nature Communications 11, 6399 (2020) [pdf] DOI: 10.1038/s41467020202803

Anomalous metallic phase in tunable destructive superconductors 
Abstract
 Multiply connected superconductors smaller than the coherence length show destructive superconductivity, characterized by reentrant quantum phase transitions driven by magnetic flux. We investigate the dependence of destructive superconductivity on flux, transverse magnetic field, temperature, and current in InAs nanowires with a surrounding epitaxial Al shell, finding excellent agreement with meanfield theory across multiple reentrant transitions. Near the crossover between destructive and nondestructive regimes, an anomalous metal phase is observed with temperatureindependent resistance, controlled over two orders of magnitude by a milliteslascale transverse magnetic field.
S. Vaitiekėnas, P. Krogstrup, C. M. Marcus Journal reference: Phys. Rev. B 101, 060507 (2020) [pdf] DOI: 10.1103/PhysRevB.101.060507

Temperature induced shifts of Yu–Shiba–Rusinov resonances in nanowirebased hybrid quantum dots 
Abstract
 The strong coupling of a superconductor to a spinful quantum dot results in YuShibaRusinov (YSR) discrete subgap excitations. In isolation and at zero temperature, the excitations are $\delta$ resonances. In transport experiments, however, they show as broad differential conductance peaks. We obtain the lineshape of the peaks and their temperature dependence in superconductorquantumdotmetal (SQDN) nanowirebased devices. Unexpectedly, we find that the peaks shift in energy with temperature, with the shift magnitude and sign depending on ground state parity and bias voltage. Additionally, we empirically find a powerlaw scaling of the peak area versus temperature. These observations are not explained by current models.
Juan Carlos Estrada Saldaña, Alexandros Vekris, Victoria Sosnovtseva, Thomas Kanne, Peter Krogstrup, Kasper GroveRasmussen, Jesper Nygård Journal reference: Commun Phys 3, 125 (2020) https://rdcu.be/b5ymM [pdf] DOI: 10.1038/s4200502003925

Absence of supercurrent sign reversal in a topological junction with a quantum dot 
Abstract
 Experimental techniques to verify Majoranas are of current interest. A prominent test is the effect of Majoranas on the Josephson current between two wires linked via a normal junction. Here, we study the case of a quantum dot connecting the two superconductors and the sign of the supercurrent in the trivial and topological regimes under grandcanonical equilibrium conditions, explicitly allowing for parity changes due to, e.g., quasiparticle poisoning. We find that the wellknown supercurrent reversal for odd occupancy of the quantum dot (pijunction) in the trivial case does not occur in the presence of Majoranas in the wires. However, we also find this to be a mere consequence of Majoranas being zero energy states. Therefore, the lack of supercurrent sign reversal can also be caused by trivial bound states, and is thus not a discriminating signature of Majoranas.
J. Schulenborg, K. Flensberg Journal reference: Phys. Rev. B 101, 014512 (2020) [pdf] DOI: 10.1103/PhysRevB.101.014512

Weak Measurement Protocols for Majorana Bound State Identification 
Abstract
 We propose a continuous weak measurement protocol testing the nonlocality of Majorana bound states through current shot noise correlations. The experimental setup contains a topological superconductor island with three normalconducting leads weakly coupled to different Majorana states. Putting one lead at finite voltage and measuring the shot noise correlations between the other two (grounded) leads, devices with true Majorana states are distinguished from those without by strong current correlations. The presence of true Majoranas manifests itself in unusually high noise levels or the near absence of noise, depending on the chosen device configuration. Monitoring the noise statistics amounts to a weak continuous measurement of the Majorana qubit and yields information similar to that of a full braiding protocol, but at much lower experimental effort. Our theory can be adapted to different platforms and should allow for clear identification of Majorana states.
Jan Manousakis, Carolin Wille, Alexander Altland, Reinhold Egger, Karsten Flensberg, Fabian Hassler Journal reference: Phys. Rev. Lett. 124, 096801 (2020) [pdf] DOI: 10.1103/PhysRevLett.124.096801

Relating Andreev Bound States and Supercurrents in Hybrid Josephson Junctions 
Abstract
 We investigate superconducting quantum interference devices consisting of two highly transmissive Josephson junctions coupled by a superconducting loop, all defined in an epitaxial InAs/Al heterostructure. A novel device design allows for independent measurements of the Andreev bound state spectrum within the normal region of a junction and the resulting currentphase relation. We show that knowledge of the Andreev bound state spectrum alone is enough to derive the independently measured phase dependent supercurrent. On the other hand, the opposite relation does not generally hold true as details of the energy spectrum are averaged out in a critical current measurement. Finally, quantitative understanding of field dependent spectrum and supercurrent require taking into account the second junction in the loop and the kinetic inductance of the epitaxial Al film.
F. Nichele, E. Portolés, A. Fornieri, A. M. Whiticar, A. C. C. Drachmann, T. Wang, G. C. Gardner, C. Thomas, A. T. Hatke, M. J. Manfra, C. M. Marcus Journal reference: Phys. Rev. Lett. 124, 226801 (2020) [pdf] DOI: 10.1103/PhysRevLett.124.226801

Suppressed Charge Dispersion via Resonant Tunneling in a SingleChannel Transmon 
Abstract
 We demonstrate strong suppression of charge dispersion in a semiconductorbased transmon qubit across Josephson resonances associated with a quantum dot in the junction. On resonance, dispersion is drastically reduced compared to conventional transmons with corresponding Josephson and charging energies. We develop a model of qubit dispersion for a singlechannel resonance, which is in quantitative agreement with experimental data.
A. Kringhøj, B. van Heck, T. W. Larsen, O. Erlandsson, D. Sabonis, P. Krogstrup, L. Casparis, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. Lett. 124, 246803 (2020) [pdf] DOI: 10.1103/PhysRevLett.124.246803

Timescales for charge transfer based operations on Majorana systems 
Abstract
 In this article we analyze the efficiency of operations based on transferring charge from a quantum dot (QD) to two coupled topological superconductors, which can be used for performing nonabelian operations on Majorana bound states (MBSs). We develop a method which allows us to describe the full timeevolution of the system as the QD energy is manipulated. Using a full counting statistics analysis, we set bounds to the operation time scales. The lower bound depends on the superconducting phase difference due to a partial decoupling of the different MBSs parity sectors, while the upper bound is set by the tunneling of quasiparticles to the MBSs. Using realistic parameters, we find the existence of a regime where the operation can be carried out with a fidelity close to unity. Finally, we propose the use of a two operations protocol to quantify the effect of the dephasing and accumulated dynamical phases, demonstrating their absence for certain superconducting phase differences.
R. Seoane Souto, K. Flensberg, M. Leijnse Journal reference: Phys. Rev. B 101, 081407 (2020) [pdf] DOI: 10.1103/PhysRevB.101.081407

Controlled dc Monitoring of a Superconducting Qubit 
Abstract
 Creating a transmon qubit using semiconductorsuperconductor hybrid materials not only provides electrostatic control of the qubit frequency, it also allows parts of the circuit to be electrically connected and disconnected in situ by operating a semiconductor region of the device as a fieldeffect transistor (FET). Here, we exploit this feature to compare in the same device characteristics of the qubit, such as frequency and relaxation time, with related transport properties such as critical supercurrent and normalstate resistance. Gradually opening the FET to the monitoring circuit allows the influence of weaktostrong DC monitoring of a live qubit to be measured. A model of this influence yields excellent agreement with experiment, demonstrating a relaxation rate mediated by a gatecontrolled environmental coupling.
A. Kringhøj, T. W. Larsen, B. van Heck, D. Sabonis, O. Erlandsson, I. Petkovic, D. I. Pikulin, P. Krogstrup, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. Lett. 124, 056801 (2020) [pdf] DOI: 10.1103/PhysRevLett.124.056801

Floquet topological insulators: from band structure engineering to novel
nonequilibrium quantum phenomena 
Abstract
 We review methods for using timeperiodic fields (e.g., laser or microwave fields) to induce nonequilibrium topological phenomena in quantum manybody systems. We discuss how such fields can be used to change the topological properties of the single particle spectrum, and key experimental demonstrations in solid state, cold atomic, and photonic systems. The single particle Floquet band structure provides a stage on which the system's dynamics play out; the crucial question is then how to obtain robust topological behaviour in the manyparticle setting. In the regime of mesoscopic transport, we discuss manifestations of topological edge states induced in the Floquet spectrum. Outside the context of mesoscopic transport, the main challenge of inducing stable topological phases in manybody Floquet systems is their tendency to absorb energy from the drive and thereby to heat up. We discuss three routes to overcoming this challenge: longlived transient dynamics and prethermalization, disorderinduced manybody localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of these regimes, and their experimental realizations.
Mark S. Rudner, Netanel H. Lindner [pdf]

ConductanceMatrix Symmetries of a ThreeTerminal Hybrid Device 
Abstract
 We present conductancematrix measurements of a threeterminal superconductorsemiconductor hybrid device consisting of two normal leads and one superconducting lead. Using a symmetry decomposition of the conductance, we find that the antisymmetric components of pairs of local and nonlocal conductances match at energies below the superconducting gap, consistent with expectations based on a noninteracting scattering matrix approach. Further, the local charge character of Andreev bound states is extracted from the symmetrydecomposed conductance data and is found to be similar at both ends of the device and tunable with gate voltage. Finally, we measure the conductance matrix as a function of magnetic field and identify correlated splittings in lowenergy features, demonstrating how conductancematrix measurements can complement traditional tunnelingprobe measurements in the search for Majorana zero modes.
G. C. Ménard, G. L. R. Anselmetti, E. A. Martinez, D. Puglia, F. K. Malinowski, J. S. Lee, S. Choi, M. Pendharkar, C. J. Palmstrøm, K. Flensberg, C. M. Marcus, L. Casparis, A. P. Higginbotham Journal reference: Phys. Rev. Lett. 124, 036802 (2020) [pdf] DOI: 10.1103/PhysRevLett.124.036802

Nonlocal Conductance Spectroscopy of Andreev Bound States: Symmetry Relations and BCS Charges 
Abstract
 Twoterminal conductance spectroscopy of superconducting devices is a common tool for probing Andreev and Majorana bound states. Here, we study theoretically a threeterminal setup, with two normal leads coupled to a grounded superconducting terminal. Using a singleelectron scattering matrix, we derive the subgap conductance matrix for the normal leads and discuss its symmetries. In particular, we show that the local and the nonlocal elements of the conductance matrix have pairwise identical antisymmetric components. Moreover, we find that the nonlocal elements are directly related to the local BCS charges of the bound states close to the normal probes and we show how the BCS charge of overlapping Majorana bound states can be extracted from experiments.
Jeroen Danon, Anna Birk Hellenes, Esben Bork Hansen, Lucas Casparis, Andrew P. Higginbotham, Karsten Flensberg Journal reference: Phys. Rev. Lett. 124, 036801 (2020) [pdf] DOI: 10.1103/PhysRevLett.124.036801

Photonassisted tunnelling of zero modes in a Majorana wire 
Abstract
 Hybrid nanowires with proximityinduced superconductivity in the topological regime host Majorana zero modes (MZMs) at their ends, and networks of such structures can produce topologically protected qubits. In a doubleisland geometry where each segment hosts a pair of MZMs, interpair coupling mixes the charge parity of the islands and opens an energy gap between the even and odd charge states at the interisland charge degeneracy. Here, we report on the spectroscopic measurement of such an energy gap in an InAs/Al doubleisland device by tracking the position of the microwaveinduced quasiparticle (qp) transitions using a radiofrequency (rf) charge sensor. In zero magnetic field, photon assisted tunneling (PAT) of Cooper pairs gives rise to resonant lines in the 2e2e periodic charge stability diagram. In the presence of a magnetic field aligned along the nanowire, resonance lines are observed parallel to the interisland charge degeneracy of the 1e1e periodic charge stability diagram, where the 1e periodicity results from a zeroenergy subgap state that emerges in magnetic field. Resonant lines in the charge stability diagram indicate coherent photon assisted tunneling of singleelectron states, changing the parity of the two islands. The dependence of resonant frequency on detuning indicates a sizable (GHzscale) hybridization of zero modes across the junction separating islands.
David M. T. van Zanten, Deividas Sabonis, Judith Suter, Jukka I. Väyrynen, Torsten Karzig, Dmitry I. Pikulin, Eoin C. T. O'Farrell, Davydas Razmadze, Karl D. Petersson, Peter Krogstrup, Charles M. Marcus Journal reference: Nature Physics (2020) [pdf] DOI: 10.1038/s4156702008580

Fluxinduced topological superconductivity in fullshell nanowires 
Abstract
 We consider a new model system supporting Majorana zero modes based on semiconductor nanowires with a full superconducting shell. We demonstrate that, in the presence of spinorbit coupling in the semiconductor induced by a radial electric field, the winding of the superconducting order parameter leads to a topological phase supporting Majorana zero modes. The topological phase persists over a large range of chemical potentials and can be induced by a predictable and weak magnetic field piercing the cylinder. The system can be readily realized in semiconductor nanowires covered by a full superconducting shell, opening a pathway for realizing topological quantum computing proposals.
Roman M. Lutchyn, Georg W. Winkler, Bernard van Heck, Torsten Karzig, Karsten Flensberg, Leonid I. Glazman, Chetan Nayak Journal reference: Science 367, eaav3392 (2020) [pdf] DOI: 10.1126/science.aav3392

Fluxinduced topological superconductivity in fullshell nanowires 
Abstract
 We demonstrate a novel means of creating Majorana zero modes using magnetic flux applied to a full superconducting shell surrounding a semiconducting nanowire core, unifying approaches based on proximitized nanowires and vortices in topological superconductors. In the destructive LittleParks regime, reentrant regions of superconductivity are associated with integer number of phase windings in the shell. Tunneling into the core reveals a hard induced gap near zero applied flux, corresponding to zero phase winding, and a gapped region with a discrete zeroenergy state for flux around {\Phi}_0 = h/2e, corresponding to 2{\pi} phase winding. Coulomb peak spacing in fullshell islands around one applied flux shows exponentially decreasing deviation from 1e periodicity with device length, consistent with the picture of Majorana modes located at the ends of the wire.
S. Vaitiekėnas, M. T. Deng, P. Krogstrup, C. M. Marcus Journal reference: Science 367, eaav3392 (2020) [pdf] DOI: 10.1126/science.aav3392

Exploring helical phases of matter in bosonic ladders 
Abstract
 2019

CurrentInduced Gap Opening in Interacting Topological Insulator Surfaces 
Abstract
 Twodimensional topological insulators (TIs) host gapless helical edge states that are predicted to support a quantized twoterminal conductance. Quantization is protected by timereversal symmetry, which forbids elastic backscattering. Paradoxically, the currentcarrying state itself breaks the timereversal symmetry that protects it. Here we show that the combination of electronelectron interactions and momentumdependent spin polarization in helical edge states gives rise to feedback through which an applied current opens a gap in the edge state dispersion, thereby breaking the protection against elastic backscattering. Currentinduced gap opening is manifested via a nonlinear contribution to the system's $IV$ characteristic, which persists down to zero temperature. We discuss prospects for realizations in recently discovered large bulk band gap TIs, and an analogous currentinduced gap opening mechanism for the surface states of threedimensional TIs.
Ajit C. Balram, Karsten Flensberg, Jens Paaske, Mark S. Rudner Journal reference: Phys. Rev. Lett. 123, 246803 (2019) [pdf] DOI: 10.1103/PhysRevLett.123.246803

Fast Charge Sensing of Si/SiGe Quantum Dots via a HighFrequency Accumulation Gate 
Abstract
 Quantum dot arrays are a versatile platform for the implementation of spin qubits, as highbandwidth sensor dots can be integrated with single, double and tripledot qubits yielding fast and highfidelity qubit readout. However, for undoped silicon devices, reflectometry off sensor ohmics suffers from the finite resistivity of the twodimensional electron gas (2DEG), and alternative readout methods are limited to measuring qubit capacitance, rather than qubit charge. By coupling a surfacemount resonant circuit to the plunger gate of a highimpedance sensor, we realized a fast charge sensing technique that is compatible with resistive 2DEGs. We demonstrate this by acquiring at high speed charge stability diagrams of double and tripledot arrays in Si/SiGe heterostructures as well as pulsedgate singleshot charge and spin readout with integration times as low as 2.4 $\mu$s.
Christian Volk, Anasua Chatterjee, Fabio Ansaloni, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Nano Letters 19, 56285633 (2019) [pdf] DOI: 10.1021/acs.nanolett.9b02149

Symmetryprotected spin gaps in quantum wires 
Abstract
 This work shows that a strongly correlated phase which is gapped to collective spin excitations but gapless to charge fluctuations emerges as a universal feature in onedimensional fermionic systems obeying certain symmetries. Namely, nanowires interacting via Coulomb repulsion which are symmetric under timereversal and spatial inversion symmetry exhibit spin gaps whenever one pair of spindegenerate subbands is occupied and an arbitrarily weak spinorbit interaction is present. This general result is independent of the details of the onedimensional confinement, the fermionic spin or nature of the spinorbit interaction. In narrowgap semiconductors, this gap may be of order 10 \textmu eV. This strongly correlated phase may be identified both via an anomalous $h/2e$ flux periodicity in AharonovBohm oscillations and $2e$ periodic Coulomb blockade, features which reflect the existence of fermionic pairing despite the absence of superconductivity and the repulsive nature of the interaction.
Tommy Li Journal reference: Phys. Rev. B 100, 155309 (2019) [pdf] DOI: 10.1103/PhysRevB.100.155309

Field theory approach to the quantum transport in Weyl semimetals 
Abstract
 We analyze the structure of the surface states and Fermi arcs of Weyl semimetals as a function of the boundary conditions parameterizing the Hamiltonian selfadjoint extensions of a minimal model with two Weyl points. These boundary conditions determine both the pseudospin polarization of the system on the surface and the shape of the associated Fermi arcs. We analytically derive the expectation values of the density profile of the surface current, we evaluate the anomalous Hall conductivity as a function of temperature and chemical potential and we discuss the surface current correlation functions and their contribution to the thermal noise. Based on a lattice variant of the model, we numerically study the surface states at zero temperature and we show that their polarization and, consequently, their transport properties, can be varied by suitable Zeeman terms localized on the surface. We also provide an estimate of the bulk conductance of the system based on the LandauerB\"uttiker approach. Finally, we analyze the surface anomalous thermal Hall conductivity and we show that the boundary properties lead to a correction of the expected universal thermal Hall conductivity, thus violating the WiedemannFranz law.
Michele Burrello, Enore Guadagnini, Luca Lepori, Mihail Mintchev Journal reference: Phys. Rev. B 100, 155131 (2019) [pdf] DOI: 10.1103/PhysRevB.100.155131

Semiconductor–Ferromagnetic Insulator–Superconductor Nanowires: Stray Field and Exchange Field 
Abstract
 Nanowires can serve as flexible substrates for hybrid epitaxial growth on selected facets, allowing for design of heterostructures with complex material combinations and geometries. In this work we report on hybrid epitaxy of semiconductor  ferromagnetic insulator  superconductor (InAs/EuS/Al) nanowire heterostructures. We study the crystal growth and complex epitaxial matching of wurtzite InAs / rocksalt EuS interfaces as well as rocksalt EuS / facecentered cubic Al interfaces. Because of the magnetic anisotropy originating from the nanowire shape, the magnetic structure of the EuS phase are easily tuned into single magnetic domains. This effect efficiently ejects the stray field lines along the nanowires. With tunnel spectroscopy measurements of the density of states, we show the material has a hard induced superconducting gap, and magnetic hysteretic evolution which indicates that the magnetic exchange fields are not negligible. These hybrid nanowires fulfil key material requirements for serving as a platform for spinbased quantum applications, such as scalable topological quantum computing.
Yu Liu, Saulius Vaitiekenas, Sara MartiSanchez, Christian Koch, Sean Hart, Zheng Cui, Thomas Kanne, Sabbir A. Khan, Rawa Tanta, Shivendra Upadhyay, Martin Espineira Cachaza, Charles M. Marcus, Jordi Arbiol, Kathryn A. Moler, Peter Krogstrup [pdf] DOI: 10.1021/acs.nanolett.9b04187 1910.03364v1 [pdf]

Band bending profile and band offset extraction at semiconductormetal
interfaces 
Abstract
 The band alignment of semiconductormetal interfaces plays a vital role in modern electronics, but remains difficult to predict theoretically and measure experimentally. For interfaces with strong band bending a main difficulty originates from the inbuilt potentials which lead to broadened and shifted band spectra in spectroscopy measurements. In this work we present a method to resolve the band alignment of buried semiconductormetal interfaces using core level photoemission spectroscopy and selfconsistent electronic structure simulations. As a proof of principle we apply the method to a clean insitu grown InAs(100)/Al interface, a system with a strong inbuilt band bending. Due to the high signaltonoise ratio of the core level spectra the proposed methodology can be used on previously inaccessible semiconductormetal interfaces and support targeted design of novel hybrid devices and form the foundation for a interface parameter database for specified synthesis processes of semiconductormetal systems.
 1910.02735v1 [pdf]

Charge and spin textures of Ising quantum Hall ferromagnet domain walls 
Abstract
 We investigate the charge and spin structures associated with arbitrary smooth polarization textures in Ising (integer) quantum Hall ferromagnets. We consider the case where the two polarizations (denoted "pseudospin" up and down) correspond to states with opposite physical spin and different Landau level indices, $n\uparrow$ and $m\downarrow$. We derive analytic expressions for the charge and spin densities, as functions of the underlying pseudospin texture, and use these results to investigate different types of linear domain walls, both analytically and numerically. We find that any smooth domain wall between two oppositely polarized domains carries a universal quantized charge dipole density proportional to the difference of Landau level indices, $nm$. Additionally, nonuniformities in the domain wall may give rise to excess net charge localized at the domain wall. Interestingly, the physical spin density associated with the domain wall generally exhibits a much more complex multipolar structure than that of the pseudospin texture. These results should for example help to elucidate the mechanisms underlying nuclear electric resonance and nuclear polarization oscillations in Ising quantum Hall systems.
Jeroen Danon, Ajit C. Balram, Samuel Sánchez, Mark S. Rudner Journal reference: Phys. Rev. B 100, 235406 (2019) [pdf] DOI: 10.1103/PhysRevB.100.235406

The antiferromagnetic phase of the Floquetdriven Hubbard model 
Abstract
 A saddle point plus fluctuations analysis of the periodically driven halffilled twodimensional Hubbard model is performed. For drive frequencies below the equilibrium gap, we find discontinuous transitions to timedependent solutions. A highly excited, generically nonthermal distribution of magnons occurs even for drive frequencies far above the gap. Above a critical drive amplitude, the lowenergy magnon distribution diverges as the frequency tends to zero and antiferromagnetism is destroyed, revealing the generic importance of collective mode excitations arising from a nonequilibrium drive.
Nicklas Walldorf, Dante M. Kennes, Jens Paaske, Andrew J. Millis Journal reference: Phys. Rev. B 100, 121110 (2019) [pdf] DOI: 10.1103/PhysRevB.100.121110

Endtoend correlated subgap states in hybrid nanowires 
Abstract
 Endtoend correlated bound states are investigated in superconductorsemiconductor hybrid nanowires at zero magnetic field. Peaks in subgap conductance are independently identified from each wire end, and a crosscorrelation function is computed that counts endtoend coincidences, averaging over thousands of subgap features. Strong correlations in a short, $300~\mathrm{nm}$ device are reduced by a factor of four in a long, $900~\mathrm{nm}$ device. In addition, subgap conductance distributions are investigated, and correlations between the left and right distributions are identified based on their mutual information.
G. L. R. Anselmetti, E. A. Martinez, G. C. Ménard, D. Puglia, F. K. Malinowski, J. S. Lee, S. Choi, M. Pendharkar, C. J. Palmstrøm, C. M. Marcus, L. Casparis, A. P. Higginbotham Journal reference: Phys. Rev. B 100, 205412 (2019) [pdf] DOI: 10.1103/PhysRevB.100.205412

Dispersive sensing in hybrid InAs/Al nanowires 
Abstract
 Dispersive charge sensing is realized in hybrid semiconductorsuperconductor nanowires in gatedefined single and doubleisland device geometries. Signaltonoise ratios (SNRs) were measured both in the frequency and time domain. Frequencydomain measurements were carried out as a function of frequency and power and yield a charge sensitivity of $1 \times 10^{3} e/\sqrt{\rm Hz}$ for an 11 MHz measurement bandwidth. Timedomain measurements yield SNR > 1 for 20 $\mu$s integration time. At zero magnetic field, photonassisted tunneling was detected dispersively in a doubleisland geometry, indicating coherent hybridization of the two superconducting islands. At an axial magnetic field of 0.6 T, subgap states are detected dispersively, demonstrating the suitability of the method for sensing in the topological regime.
Deividas Sabonis, Eoin C. T. O'Farrell, Davydas Razmadze, David M. T. van Zanten, Judith Suter, Peter Krogstrup, Charles M. Marcus Journal reference: Appl. Phys. Lett. 115, 102601 (2019) [pdf] DOI: 10.1063/1.5116377

Anomalous Floquet insulators 
Abstract
 We demonstrate the existence of a twodimensional anomalous Floquet insulator (AFI) phase: an interacting (periodicallydriven) nonequilibrium topological phase of matter with no counterpart in equilibrium. The AFI is characterized by a manybody localized bulk, exhibiting nontrivial micromotion within a driving period, and delocalized (thermalizing) chiral states at its boundaries. For a geometry without edges, we argue analytically that the bulk may be manybody localized in the presence of interactions, deriving conditions where stability is expected. We investigate the interplay between the thermalizing edge and the localized bulk via numerical simulations of an AFI in a geometry with edges. We find that nonuniform particle density profiles remain stable in the bulk up to the longest timescales that we can access, while the propagating edge states persist and thermalize, despite being coupled to the bulk. These findings open the possibility of observing quantized edge transport in interacting systems at high temperature. The analytical approach introduced in this paper can be used to study the stability of other anomalous Floquet phases.
Frederik Nathan, Dmitry Abanin, Erez Berg, Netanel H. Lindner, Mark S. Rudner Journal reference: Phys. Rev. B 99, 195133 (2019) [pdf] DOI: 10.1103/PhysRevB.99.195133

Fidelity and visibility loss in Majorana qubits by entanglement with environmental modes 
Abstract
 We study the dynamics and readout of topological qubits encoded by zeroenergy Majorana bound states in a topological superconductor. We take into account bosonic modes due to the electromagnetic environment which couple the Majorana manifold to abovegap continuum quasiparticles. This coupling causes the degenerate ground state of the topological superconductor to be dressed in a polaronlike manner by quasiparticle states and bosons, and the system to become gapless. Topological protection and hence full coherence is only maintained if the qubit is operated and read out within the lowenergy spectrum of the dressed states. We discuss reduction of fidelity and/or visibility if this condition is violated by a quantumdot readout that couples to the bare (undressed) Majorana modes. For a projective measurement of the bare Majorana basis, we formulate a BlochRedfield approach that is valid for weak Majoranaenvironment coupling and takes into account constraints imposed by fermionnumberparity conservation. Within the Markovian approximation, our results essentially confirm earlier theories of finitetemperature decoherence based on Fermi's golden rule. However, the full nonMarkovian dynamics reveals, in addition, the fidelity reduction by a projective measurement. Using a spinless nanowire model with $p$wave pairing, we provide quantitative results characterizing these effects.
Morten I. K. Munk, Reinhold Egger, Karsten Flensberg Journal reference: Phys. Rev. B 99, 155419 (2019) [pdf] DOI: 10.1103/PhysRevB.99.155419

InPlane Magnetoconductance Mapping of InSb Quantum Wells 
Abstract
 Inplane magnetoconductance of InSb quantum wells (QW) containing a two dimensional electron gas (2DEG) is presented. Using a vector magnet, we created a magnetoconductance map which shows the suppression of weak antilocalization (WAL) as a function of applied field. By fitting the inplane field response of the 2DEG, we estimate material disorder and gfactor as a function of crystal direction. The inplane WAL suppression is found to be dominated by the Zeeman effect and to show a small crystalorientationdependent anistropy in disorder and gfactor. These measurements show the utility of multidirectional measurement of magnetoconductance in analyzing material properties.
 1902.07570v1 [pdf]
J. T. Mlack, K. S. Wickramasinghe, T. D. Mishima, M. B. Santos, C. M. Marcus [pdf]

Suppressing quasiparticle poisoning with a voltagecontrolled filter 
Abstract
 We study singleelectron charging events in an Al/InAs nanowire hybrid system with deliberately introduced gapless regions. The occupancy of a Coulomb island is detected using a nearby radiofrequency quantum dot as a charge sensor. We demonstrate that a 1 micron gapped segment of the wire can be used to efficiently suppress single electron poisoning of the gapless region and therefore protect the parity of the island while maintaining good electrical contact with a normal lead. In the absence of protection by charging energy, the 1e switching rate can be reduced below 200 per second. In the same configuration, we observe strong quantum charge fluctuations due to exchange of electron pairs between the island and the lead. The magnetic field dependence of the poisoning rate yields a zerofield superconducting coherence length of ~ 90 nm.
Gerbold C. Ménard, Filip K. Malinowski, Denise Puglia, Dmitry I. Pikulin, Torsten Karzig, Bela Bauer, Peter Krogstrup, Charles M. Marcus Journal reference: Phys. Rev. B 100, 165307 (2019) [pdf] DOI: 10.1103/PhysRevB.100.165307

RadioFrequency Methods for MajoranaBased Quantum Devices: Fast Charge Sensing and PhaseDiagram Mapping 
Abstract
 Radiofrequency (RF) reflectometry is implemented in hybrid semiconductorsuperconductor nanowire systems designed to probe Majorana zero modes. Two approaches are presented. In the first, hybrid nanowirebased devices are part of a resonant circuit, allowing conductance to be measured as a function of several gate voltages ~40 times faster than using conventional lowfrequency lockin methods. In the second, nanowire devices are capacitively coupled to a nearby RF singleelectron transistor made from a separate nanowire, allowing RF detection of charge, including chargeonly measurement of the crossover from 2e interisland charge transitions at zero magnetic field to 1e transitions at axial magnetic fields above 0.6 T, where a topological state is expected. Singleelectron sensing yields signaltonoise exceeding 3 and visibility 99.8% for a measurement time of 1 {\mu}s.
Davydas Razmadze, Deividas Sabonis, Filip K. Malinowski, Gerbold C. Menard, Sebastian Pauka, Hung Nguyen, David M. T. van Zanten, Eoin C. T. O'Farrell, Judith Suter, Peter Krogstrup, Ferdinand Kuemmeth, Charles M. Marcus Journal reference: Phys. Rev. Applied 11, 064011 (2019) [pdf] DOI: 10.1103/PhysRevApplied.11.064011

Interplay between magnetic and vestigial nematic orders in the layered

Abstract
 We study the layered $J_1$$J_2$ classical Heisenberg model on the square lattice using a selfconsistent bond theory. We derive the phase diagram for fixed $J_1$ as a function of temperature $T$, $J_2$ and interplane coupling $J_z$. Broad regions of (anti)ferromagnetic and stripe order are found, and are separated by a firstorder transition near $J_2\approx 0.5$ (in units of $J_1$). Within the stripe phase the magnetic and vestigial nematic transitions occur simultaneously in firstorder fashion for strong $J_z$. For weaker $J_z$ there is in addition, for $J_2^*<j_2 <="<" j_2^{**}$,="J_2^{**}$," an="an" intermediate="intermediate" regime="regime" of="of" split="split" transitions="transitions" implying="implying" a="a" finite="finite" temperature="temperature" region="region" with="with" nematic="nematic" order="order" but="but" no="no" longrange="longrange" stripe="stripe" magnetic="magnetic" order.="order." in="In" this="this" split="split" regime,="regime," the="the" order="order" of="of" the="the" transitions="transitions" depends="depends" sensitively="sensitively" on="on" the="the" deviation="deviation" from="from" $j_2^*$="$J_2^*$" and="and" $j_2^{**}$,="$J_2^{**}$," with="with" split="split" secondorder="secondorder" transitions="transitions" predominating="predominating" for="for" $j_2^*="$J_2^*" \ll="\ll" j_2="J_2" \ll="\ll" j_2^{**}$.="J_2^{**}$." we="We" find="find" that="that" the="the" value="value" of="of" $j_2^*$="$J_2^*$" depends="depends" weakly="weakly" on="on" the="the" interplane="interplane" coupling="coupling" and="and" is="is" just="just" slightly="slightly" larger="larger" than="than" $0.5$="$0.5$" for="for" $j_z="$J_z" \lesssim="\lesssim" 0.01$.="0.01$." in="In" contrast="contrast" the="the" value="value" of="of" $j_2^{**}$="$J_2^{**}$" increases="increases" quickly="quickly" from="from" $j_2^*$="$J_2^*$" at="at" $j_z="$J_z" \lesssim="\lesssim" 0.01$="0.01$" as="as" the="the" interplane="interplane" coupling="coupling" is="is" further="further" reduced.="reduced." in="In" addition,="addition," the="the" magnetic="magnetic" correlation="correlation" length="length" is="is" shown="shown" to="to" directly="directly" depend="depend" on="on" the="the" nematic="nematic" order="order" parameter="parameter" and="and" thus="thus" exhibits="exhibits" a="a" sharp="sharp" increase="increase" (or="(or" jump)="jump)" upon="upon" entering="entering" the="the" nematic="nematic" phase.="phase." our="Our" results="results" are="are" broadly="broadly" consistent="consistent" with="with" predictions="predictions" based="based" on="on" itinerant="itinerant" electron="electron" models="models" of="of" the="the" ironbased="ironbased" superconductors="superconductors" in="In" the="the" normalstate,="normalstate," and="and" thus="thus" help="help" substantiate="substantiate" a="a" classical="classical" spin="spin" framework="framework" for="for" providing="providing" a="a" phenomenological="phenomenological" description="description" of="of" their="their" magnetic="magnetic" properties.
Olav F. Syljuåsen, Jens Paaske, Michael Schecter Journal reference: Phys. Rev. B 99, 174404 (2019) [pdf] DOI: 10.1103/PhysRevB.99.174404

Coulombinteractioninduced Majorana edge modes in nanowires 
Abstract
 We show that Majorana edge modes appear in a strongly correlated phase of semiconducting nanowires with discrete rotational symmetry in the cross section. These modes exist in the absence of spinorbit coupling, magnetic fields and superconductivity. They appear purely due to the combination of the threedimensional Coulomb interaction and orbital physics, which generates a fermionic condensate exhibiting a topological ground state degeneracy in a sector of the spectrum which is gapped to continuum modes. The gap can be comparable in magnitude to the topological superconducting gap in other solidstate candidate systems for Majorana edge modes, and may similarly be probed via tunnel spectroscopy.
Tommy Li, Michele Burrello, Karsten Flensberg Journal reference: Phys. Rev. B 100, 045305 (2019) [pdf] DOI: 10.1103/PhysRevB.100.045305

Coupling of shells in a carbon nanotube quantum dot 
Abstract
 We systematically study the coupling of longitudinal modes (shells) in a carbon nanotube quantum dot. Inelastic cotunneling spectroscopy is used to probe the excitation spectrum in parallel, perpendicular and rotating magnetic fields. The data is compared to a theoretical model including coupling between shells, induced by atomically sharp disorder in the nanotube. The calculated excitation spectra show good correspondence with experimental data.
M. C. Hels, T. S. Jespersen, J. Nygård, K. GroveRasmussen Journal reference: Phys. Rev. B 99, 035422 (2019) [pdf] DOI: 10.1103/PhysRevB.99.035422

Evidence of topological superconductivity in planar Josephson junctions 
Abstract
 Majorana zero modes are quasiparticle states localized at the boundaries of topological superconductors that are expected to be ideal building blocks for faulttolerant quantum computing. Several observations of zerobias conductance peaks measured in tunneling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor/semiconductor nanowires. On the other hand, two dimensional systems offer the alternative approach to confine Ma jorana channels within planar Josephson junctions, in which the phase difference {\phi} between the superconducting leads represents an additional tuning knob predicted to drive the system into the topological phase at lower magnetic fields. Here, we report the observation of phasedependent zerobias conductance peaks measured by tunneling spectroscopy at the end of Josephson junctions realized on a InAs/Al heterostructure. Biasing the junction to {\phi} ~ {\pi} significantly reduces the critical field at which the zerobias peak appears, with respect to {\phi} = 0. The phase and magnetic field dependence of the zeroenergy states is consistent with a model of Majorana zero modes in finitesize Josephson junctions. Besides providing experimental evidence of phasetuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures and scalable to complex geometries needed for topological quantum computing.
Antonio Fornieri, Alexander M. Whiticar, F. Setiawan, Elías Portolés Marín, Asbjørn C. C. Drachmann, Anna Keselman, Sergei Gronin, Candice Thomas, Tian Wang, Ray Kallaher, Geoffrey C. Gardner, Erez Berg, Michael J. Manfra, Ady Stern, Charles M. Marcus, Fabrizio Nichele Journal reference: Nature 569, 8992 (2019) [pdf] DOI: 10.1038/s4158601910688

Coulomb Blockade of a Nearly Open Majorana Island 
Abstract
 We consider the groundstate energy and the spectrum of the lowenergy excitations of a Majorana island formed of topological superconductors connected by a singlemode junction of arbitrary transmission. Coulomb blockade results in $e$periodic modulation of the energies with the gateinduced charge. We find the amplitude of modulation as a function of reflection coefficient ${\cal R}$. The amplitude scales as $\sqrt{\cal R}$ in the limit ${\cal R}\to 0$. At larger ${\cal R}$, the dependence of the amplitude on the Josephson and charging energies is similar to that of a conventionalsuperconductor Cooperpair box. The crossover value of ${\cal R}$ is small and depends on the ratio of the charging energy to superconducting gap.
Dmitry I. Pikulin, Karsten Flensberg, Leonid I. Glazman, Manuel Houzet, Roman M. Lutchyn Journal reference: Phys. Rev. Lett. 122, 016801 (2019) [pdf] DOI: 10.1103/PhysRevLett.122.016801

Fast spin exchange across a multielectron mediator 
Abstract
 The Heisenberg exchange interaction between neighboring quantum dots allows precise voltage control over spin dynamics, due to the ability to precisely control the overlap of orbital wavefunctions by gate electrodes. This allows the study of fundamental electronic phenomena and finds applications in quantum information processing. Although spinbased quantum circuits based on shortrange exchange interactions are possible, the development of scalable, longerrange coupling schemes constitutes a critical challenge within the spinqubit community. Approaches based on capacitative coupling and cavitymediated interactions effectively couple spin qubits to the charge degree of freedom, making them susceptible to electricallyinduced decoherence. The alternative is to extend the range of the Heisenberg exchange interaction by means of a quantum mediator. Here, we show that a multielectron quantum dot with 50100 electrons serves as an excellent mediator, preserving speed and coherence of the resulting spinspin coupling while providing several functionalities that are of practical importance. These include speed (mediated twoqubit rates up to several gigahertz), distance (of order of a micrometer), voltage control, possibility of sweet spot operation (reducing susceptibility to charge noise), and reversal of the interaction sign (useful for dynamical decoupling from noise).
Filip K. Malinowski, Frederico Martins, Thomas B. Smith, Stephen D. Bartlett, Andrew C. Doherty, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Nature Communications 10, 1196 (2019) [pdf] DOI: 10.1038/s4146701909194x

Voltagecontrolled superconducting quantum bus 
Abstract
 We demonstrate the ability of an epitaxial semiconductorsuperconductor nanowire to serve as a fieldeffect switch to tune a superconducting cavity. Two superconducting gatemon qubits are coupled to the cavity, which acts as a quantum bus. Using a gate voltage to control the superconducting switch yields up to a factor of 8 change in qubitqubit coupling between the on and off states without detrimental effect on qubit coherence. Highbandwidth operation of the coupling switch on nanosecond timescales degrades qubit coherence.
L. Casparis, N. J. Pearson, A. Kringhøj, T. W. Larsen, F. Kuemmeth, J. Nygård, P. Krogstrup, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. B 99, 085434 (2019) [pdf] DOI: 10.1103/PhysRevB.99.085434

CurrentInduced Gap Opening in Interacting Topological Insulator Surfaces 
Abstract
 2018

Supercurrent in a Double Quantum Dot 
Abstract
 We demonstrate the Josephson effect in a serial double quantum dot defined in a nanowire with epitaxial superconducting leads. The supercurrent stability diagram adopts a honeycomb pattern with electronhole and leftright reflection symmetry. We observe sharp discontinuities in the magnitude of the critical current, $I_c$, as a function of dot occupation, related to doublet to singlet ground state transitions. Detuning of the energy levels offers a tuning knob for $I_c$, which attains a maximum at zero detuning. The consistency between experiment and theory indicates that our device is a faithful realization of the twoimpurity Anderson model.
J. C. Estrada Saldaña, A. Vekris, G. Steffensen, R. Žitko, P. Krogstrup, J. Paaske, K. GroveRasmussen, J. Nygård Journal reference: Phys. Rev. Lett. 121, 257701 (2018) [pdf] DOI: 10.1103/PhysRevLett.121.257701

Nonlocality of Majorana modes in hybrid nanowires 
Abstract
 Spatial separation of Majorana zero modes distinguishes trivial from topological midgap states and is key to topological protection in quantum computing applications. Although signatures of Majorana zero modes in tunneling spectroscopy have been reported in numerous studies, a quantitative measure of the degree of separation, or nonlocality, of the emergent zero modes has not been reported. Here, we present results of an experimental study of nonlocality of emergent zero modes in superconductorsemiconductor hybrid nanowire devices. The approach takes advantage of recent theory showing that nonlocality can be measured from splitting due to hybridization of the zero mode in resonance with a quantum dot state at one end of the nanowire. From these splittings as well as anticrossing of the dot states, measured for even and odd occupied quantum dot states, we extract both the degree of nonlocality of the emergent zero mode, as well as the spin canting angles of the nonlocal zero mode. Depending on the device measured, we obtain either a moderate degree of nonlocality, suggesting a partially separated Andreev subgap state, or a highly nonlocal state consistent with a welldeveloped Majorana mode.
M. T. Deng, S. Vaitiekénas, E. Prada, P. SanJose, J. Nygård, P. Krogstrup, R. Aguado, C. M. Marcus Journal reference: Phys. Rev. B 98, 085125 (2018) [pdf] DOI: 10.1103/PhysRevB.98.085125

Dyonic zeroenergy modes 
Abstract
 Onedimensional systems with topological order are intimately related to the appearance of zeroenergy modes localized on their boundaries. The most common example is the Kitaev chain, which displays Majorana zeroenergy modes and it is characterized by a twofold ground state degeneracy related to the global $\mathbb{Z}_2$ symmetry associated with fermionic parity. By extending the symmetry to the $\mathbb{Z}_N$ group, it is possible to engineer systems hosting topological parafermionic modes. In this work, we address onedimensional systems with a generic discrete symmetry group $G$. We define a ladder model of gauge fluxes that generalizes the Ising and Potts models and displays a symmetry broken phase. Through a nonAbelian JordanWigner transformation, we map this flux ladder into a model of dyonic operators, defined by the group elements and irreducible representations of $G$. We show that the soobtained dyonic model has topological order, with zeroenergy modes localized at its boundary. These dyonic zeroenergy modes are in general weak topological modes, but strong dyonic zero modes appear when suitable positiondependent couplings are considered.
Morten I. K. Munk, Asbjørn Rasmussen, Michele Burrello Journal reference: Phys. Rev. B 98, 245135 (2018) [pdf] DOI: 10.1103/PhysRevB.98.245135

Effective

Abstract
 We use the effective gfactor of subgap states, g*, in hybrid InAs nanowires with an epitaxial Al shell to investigate how the superconducting density of states is distributed between the semiconductor core and the metallic shell. We find a steplike reduction of g* and improved hard gap with reduced carrier density in the nanowire, controlled by gate voltage. These observations are relevant for Majorana devices, which require tunable carrier density and g* exceeding the gfactor of the proximitizing superconductor. Additionally, we observe the closing and reopening of a gap in the subgap spectrum coincident with the appearance of a zerobias conductance peak.
S. Vaitiekėnas, M. T. Deng, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Phys. Rev. Lett. 121, 037703 (2018) [pdf] DOI: 10.1103/PhysRevLett.121.037703

Strainenhanced optical absorbance of topological insulator films 
Abstract
 Topological insulator films are promising materials for optoelectronics due to a strong optical absorption and a thickness dependent band gap of the topological surface states. They are superior candidates for photodetector applications in the THzinfrared spectrum, with a potential performance higher than graphene. Using a firstprinciples $k\cdot p$ Hamiltonian, incorporating all symmetryallowed terms to second order in the wave vector $k$, first order in the strain $\epsilon$ and of order $\epsilon k$, we demonstrate significantly improved optoelectronic performance due to strain. For Bi$_2$Se$_3$ films of variable thickness, the surface state band gap, and thereby the optical absorption, can be effectively tuned by application of uniaxial strain, $\epsilon_{zz}$, leading to a divergent band edge absorbance for $\epsilon_{zz}\gtrsim 6\%$. Shear strain breaks the crystal symmetry and leads to an absorbance varying significantly with polarization direction. Remarkably, the directional average of the absorbance always increases with strain, independent of material parameters.
Mathias Rosdahl Brems, Jens Paaske, Anders Mathias Lunde, Morten Willatzen Journal reference: Phys. Rev. B 97, 081402(R) (2018) [pdf] DOI: 10.1103/PhysRevB.97.081402

Hybridization at SuperconductorSemiconductor Interfaces 
Abstract
 Hybrid superconductorsemiconductor devices are currently one of the most promising platforms for realizing Majorana zero modes. Their topological properties are controlled by the band alignment of the two materials, as well as the electrostatic environment, which are currently not well understood. Here, we pursue to fill in this gap and address the role of band bending and superconductorsemiconductor hybridization in such devices by analyzing a gated single AlInAs interface using a selfconsistent SchrodingerPoisson approach. Our numerical analysis shows that the band bending leads to an interface quantum well, which localizes the charge in the system near the superconductorsemiconductor interface. We investigate the hybrid band structure and analyze its response to varying the gate voltage and thickness of the Al layer. This is done by studying the hybridization degrees of the individual subbands, which determine the induced pairing and effective $g$factors. The numerical results are backed by approximate analytical expressions which further clarify key aspects of the band structure. We find that one can obtain states with strong superconductorsemiconductor hybridization at the Fermi energy, but this requires a fine balance of parameters, with the most important constraint being on the width of the Al layer. In fact, in the regime of interest, we find an almost periodic dependence of the hybridization degree on the Al width, with a period roughly equal to the thickness of an Al monolayer. This implies that disorder and shape irregularities, present in realistic devices, may play an important role for averaging out this sensitivity and, thus, may be necessary for stabilizing the topological phase.
August E. G. Mikkelsen, Panagiotis Kotetes, Peter Krogstrup, Karsten Flensberg Journal reference: Phys. Rev. X 8, 031040 (2018) [pdf] DOI: 10.1103/PhysRevX.8.031040

FourMajorana qubit with charge readout: Dynamics and decoherence 
Abstract
 We present a theoretical analysis of a Majoranabased qubit consisting of two topological superconducting islands connected via a Josephson junction. The qubit is operated by electrostatic gates which control the coupling of two of the four Majorana zero modes. At the end of the operation, readout is performed in the charge basis. Even though the operations are not topologically protected, the proposed experiment can potentially shed light on the coherence of the parity degree of freedom in Majorana devices and serve as a first step towards topological Majorana qubits. We discuss in detail the chargestability diagram and its use for characterizing the parameters of the devices, including the overlap of the Majorana edge states. We describe the multilevel spectral properties of the system and present a detailed study of its controlled coherent oscillations, as well as decoherence resulting from coupling to a nonMarkovian environment. In particular, we study a gatecontrolled protocol where conversion between Coulombblockade and transmon regimes generates coherent oscillations of the qubit state due to the overlap of Majorana modes. We show that, in addition to fluctuations of the Majorana coupling, considerable measurement errors may be accumulated during the conversion intervals when electrostatic fluctuations in the superconducting islands are present. These results are also relevant for several proposed implementations of topological qubits which rely on readout based on charge detection.
Tommy Li, William A. Coish, Michael Hell, Karsten Flensberg, Martin Leijnse Journal reference: Phys. Rev. B 98, 205403 (2018) [pdf] DOI: 10.1103/PhysRevB.98.205403

Hybridization of Subgap States in OneDimensional SuperconductorSemiconductor Coulomb Islands 
Abstract
 We present measurements of onedimensional superconductorsemiconductor Coulomb islands, fabricated by gate confinement of a twodimensional InAs heterostructure with an epitaxial Al layer. When tuned via electrostatic side gates to regimes without subgap states, Coulomb blockade reveals Cooperpair mediated transport. When subgap states are present, Coulomb peak positions and heights oscillate in a correlated way with magnetic field and gate voltage, as predicted theoretically, with (anti) crossings in (parallel) transverse magnetic field indicating Rashbatype spinorbit coupling. Overall results are consistent with a picture of overlapping Majorana zero modes in finite wires.
E. C. T. O'Farrell, A. C. C. Drachmann, M. Hell, A. Fornieri, A. M. Whiticar, E. B. Hansen, S. Gronin, G. C. Gardener, C. Thomas, M. J. Manfra, K. Flensberg, C. M. Marcus, F. Nichele Journal reference: Phys. Rev. Lett. 121, 256803 (2018) [pdf] DOI: 10.1103/PhysRevLett.121.256803

Field effect enhancement in buffered quantum nanowire networks 
Abstract
 IIIV semiconductor nanowires have shown great potential in various quantum transport experiments. However, realizing a scalable highquality nanowirebased platform that could lead to quantum information applications has been challenging. Here, we study the potential of selective area growth by molecular beam epitaxy of InAs nanowire networks grown on GaAsbased buffer layers. The buffered geometry allows for substantial elastic strain relaxation and a strong enhancement of field effect mobility. We show that the networks possess strong spinorbit interaction and long phase coherence lengths with a temperature dependence indicating ballistic transport. With these findings, and the compatibility of the growth method with hybrid epitaxy, we conclude that the material platform fulfills the requirements for a wide range of quantum experiments and applications.
Filip Krizek, Joachim E. Sestoft, Pavel Aseev, Sara MartiSanchez, Saulius Vaitiekenas, Lucas Casparis, Sabbir A. Khan, Yu Liu, Tomas Stankevic, Alexander M. Whiticar, Alexandra Fursina, Frenk Boekhout, Rene Koops, Emanuele Uccelli, Leo P. Kouwenhoven, Charles M. Marcus, Jordi Arbiol, Peter Krogstrup Journal reference: Phys. Rev. Materials 2, 093401 (2018) [pdf] DOI: 10.1103/PhysRevMaterials.2.093401

Symmetry analysis of strain, electric and magnetic fields in the Bi

Abstract
 Based on group theoretical arguments we derive the most general Hamiltonian for the $\text{Bi}_2\text{Se}_3$class of materials including terms to third order in the wave vector, first order in electric and magnetic fields, first order in strain and first order in both strain and wave vector. We determine analytically the effects of strain on the electronic structure of $\text{Bi}_2\text{Se}_3$. For the most experimentally relevant surface termination we analytically derive the surface state spectrum, revealing an anisotropic Dirac cone with elliptical constant energy counturs giving rise to different velocities in different inplane directions. The spinmomentum locking of strained $\text{Bi}_2\text{Se}_3$ is shown to be modified and for some strain configurations we see a nonzero spin component perpendicular to the surface. Hence, strain control can be used to manipulate the spin degree of freedom via the spinorbit coupling. We show that for a thin film of $\text{Bi}_2\text{Se}_3$ the surface state band gap induced by coupling between the opposite surfaces changes opposite to the bulk band gap under strain. Tuning the surface state band gap by strain, gives new possibilities for the experimental investigation of the thickness dependent gap and optimization of optical properties relevant for, e.g., photodetector and energy harvesting applications. We finally derive analytical expressions for the effective mass tensor of the Bi$_2$Se$_3$ class of materials as a function of strain and electric field.
Mathias Rosdahl Jensen, Jens Paaske, Anders Mathias Lunde, Morten Willatzen Journal reference: New J. Phys. 20 (2018) 053041 [pdf] DOI: 10.1088/13672630/aabcfc

Distinguishing Majorana bound states from localized Andreev bound states by interferometry 
Abstract
 Experimental evidence for Majorana bound states (MBSs) is so far mainly based on the robustness of a zerobias conductance peak. However, similar features can also arise due to Andreev bound states (ABSs) localized at the end of an island. We show that these two scenarios can be distinguished by an interferometry experiment based on embedding a Coulombblockaded island into an AharonovBohm ring. For two ABSs, when the ground state is nearly degenerate, cotunneling can change the state of the island and interference is suppressed. By contrast, for two MBSs the ground state is nondegenerate and cotunneling has to preserve the island state, which leads to $h / e$periodic conductance oscillations with magnetic flux. Such interference setups can be realized with semiconducting nanowires or twodimensional electron gases with proximityinduced superconductivity and may also be a useful spectroscopic tool for parityflip mechanisms.
Michael Hell, Karsten Flensberg, Martin Leijnse Journal reference: Phys. Rev. B 97, 161401 (2018) [pdf] DOI: 10.1103/PhysRevB.97.161401

Probing electronhole components of subgap states in Coulomb blockaded Majorana islands 
Abstract
 Recent tunneling spectroscopy experiments in semiconducting nanowires with proximityinduced superconductivity have reported robust zerobias conductance peaks. Such a feature can be compatible with the existence of topological Majorana bound states (MBSs) and with a trivial Andreev bound state (ABS) near zero energy. Here, we argue that additional information, that can distinguish between the two cases, can be extracted from Coulombblockade experiments of Majorana islands. The key is the ratio of peak heights of consecutive conductance peaks give information about the electron and hole components of the lowestenergy subgap state. In the MBS case, this ratio goes to one half for long wires, while for short wires with finite MBS overlap it oscillates a function of Zeeman energy with the same period as the MBS energy splitting. We explain how the additional information might help to distinguish a trivial ABS at zero energy from a true MBS and show case examples.
Esben Bork Hansen, Jeroen Danon, Karsten Flensberg Journal reference: Phys. Rev. B 97, 041411 (2018) [pdf] DOI: 10.1103/PhysRevB.97.041411

Engineering hybrid epitaxial InAsSb/Al nanowires for stronger topological protection 
Abstract
 The combination of strong spinorbit coupling, large $g$factors, and the coupling to a superconductor can be used to create a topologically protected state in a semiconductor nanowire. Here we report on growth and characterization of hybrid epitaxial InAsSb/Al nanowires, with varying composition and crystal structure. We find the strongest spinorbit interaction at intermediate compositions in zincblende InAs$_{1x}$Sb$_{x}$ nanowires, exceeding that of both InAs and InSb materials, confirming recent theoretical studies \cite{winkler2016topological}. We show that the epitaxial InAsSb/Al interfaces allows for a hard induced superconducting gap and 2$e$ transport in Coulomb charging experiments, similar to experiments on InAs/Al and InSb/Al materials, and find measurements consistent with topological phase transitions at low magnetic fields due to large effective $g$factors. Finally we present a method to grow pure wurtzite InAsSb nanowires which are predicted to exhibit even stronger spinorbit coupling than the zincblende structure.
Joachim E. Sestoft, Thomas Kanne, Aske Nørskov Gejl, Merlin von Soosten, Jeremy S. Yodh, Daniel Sherman, Brian Tarasinski, Michael Wimmer, Erik Johnson, Mingtang Deng, Jesper Nygård, Thomas Sand Jespersen, Charles M. Marcus, Peter Krogstrup Journal reference: Phys. Rev. Materials 2, 044202 (2018) [pdf] DOI: 10.1103/PhysRevMaterials.2.044202

Superconducting gatemon qubit based on a proximitized twodimensional electron gas 
Abstract
 The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies and interqubit coupling strengths, to the gain of parametric amplifiers for quantumlimited readout. The inductance is either set by tailoring the metaloxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices (SQUIDs) with local currentbiased flux lines. JJs based on superconductorsemiconductor hybrids represent a tantalizing allelectric alternative. The gatemon is a recently developed transmon variant which employs locally gated nanowire (NW) superconductorsemiconductor JJs for qubit control. Here, we go beyond proofofconcept and demonstrate that semiconducting channels etched from a waferscale twodimensional electron gas (2DEG) are a suitable platform for building a scalable gatemonbased quantum computer. We show 2DEG gatemons meet the requirements by performing voltagecontrolled single qubit rotations and twoqubit swap operations. We measure qubit coherence times up to ~2 us, limited by dielectric loss in the 2DEG host substrate.
Lucas Casparis, Malcolm R. Connolly, Morten Kjaergaard, Natalie J. Pearson, Anders Kringhøj, Thorvald W. Larsen, Ferdinand Kuemmeth, Tiantian Wang, Candice Thomas, Sergei Gronin, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Karl D. Petersson Journal reference: Nature Nanotechnology 13, 915 (2018) [pdf] DOI: 10.1038/s415650180207y

Yu–Shiba–Rusinov screening of spins in double quantum dots 
Abstract
 A magnetic impurity coupled to a superconductor gives rise to a YuShibaRusinov (YSR) state inside the superconducting energy gap. With increasing exchange coupling the excitation energy of this state eventually crosses zero and the system switches to a YSR groundstate with bound quasiparticles screening the impurity spin by $\hbar/2$. Here we explore InAs nanowire double quantum dots tunnel coupled to a superconductor and demonstrate YSR screening of spin1/2 and spin1 states. Gating the double dot through 9 different charge states, we show that the honeycomb pattern of zerobias conductance peaks, archetypal of double dots coupled to normal leads, is replaced by lines of zeroenergy YSR states. These enclose regions of YSRscreened dot spins displaying distinctive spectral features, and their characteristic shape and topology change markedly with tunnel coupling strengths. We find excellent agreement with a simple zerobandwidth approximation, and with numerical renormalization group calculations for the twoorbital Anderson model.
K. GroveRasmussen, G. Steffensen, A. Jellinggaard, M. H. Madsen, R. Žitko, J. Paaske, J. Nygård Journal reference: Nature Communications 9, 2376 (2018) [pdf] DOI: 10.1038/s4146701804683x

ManyBody Dynamics and Gap Opening in Interacting Periodically Driven Systems 
Abstract
 We study the transient dynamics in a twodimensional system of interacting Dirac fermions subject to a quenched drive with circularly polarized light. In the absence of interactions, the drive opens a gap at the Dirac point in the quasienergy spectrum, inducing nontrivial band topology. Here we investigate the dynamics of this gap opening process in the presence of interactions, as captured by the generalized spectral function and correlators probed by photoemission experiments. Through a mechanism akin to that known for equilibrium systems, interactions renormalize and enhance the induced gap over its value for the noninteracting system. We additionally study the heating that naturally accompanies driving in the interacting system, and discuss the regimes where dynamical gap emergence and enhancement can be probed before heating becomes significant.
Ervand Kandelaki, Mark S. Rudner Journal reference: Phys. Rev. Lett. 121, 036801 (2018) [pdf] DOI: 10.1103/PhysRevLett.121.036801

Spin of a Multielectron Quantum Dot and Its Interaction with a Neighboring Electron 
Abstract
 We investigate the spin of a multielectron GaAs quantum dot in a sequence of nine charge occupancies, by exchange coupling the multielectron dot to a neighboring twoelectron double quantum dot. For all nine occupancies, we make use of a leakage spectroscopy technique to reconstruct the spectrum of spin states in the vicinity of the interdot charge transition between a single and a multielectron quantum dot. In the same regime we also perform timeresolved measurements of coherent exchange oscillations between the single and multielectron quantum dot. With these measurements, we identify distinct characteristics of the multielectron spin state, depending on whether the dot's occupancy is even or odd. For three out of four even occupancies we do not observe any exchange interaction with the single quantum dot, indicating a spin0 ground state. For the one remaining even occupancy, we observe an exchange interaction that we associate with a spin1 multielectron quantum dot ground state. For all five of the odd occupancies, we observe an exchange interaction associated with a spin1/2 ground state. For three of these odd occupancies, we clearly demonstrate that the exchange interaction changes sign in the vicinity of the charge transition. For one of these, the exchange interaction is negative (i.e. tripletpreferring) beyond the interdot charge transition, consistent with the observed spin1 for the next (even) occupancy. Our experimental results are interpreted through the use of a Hubbard model involving two orbitals of the multielectron quantum dot. Allowing for the spin correlation energy (i.e. including a term favoring Hund's rules) and different tunnel coupling to different orbitals, we qualitatively reproduce the measured exchange profiles for all occupancies.
Filip K. Malinowski, Frederico Martins, Thomas B. Smith, Stephen D. Bartlett, Andrew C. Doherty, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. X 8, 011045 (2018) [pdf] DOI: 10.1103/PhysRevX.8.011045

Anharmonicity of a superconducting qubit with a fewmode Josephson junction 
Abstract
 Coherent operation of gatevoltagecontrolled hybrid transmon qubits (gatemons) based on semiconductor nanowires was recently demonstrated. Here we experimentally investigate the anharmonicity in epitaxial InAsAl Josephson junctions, a key parameter for their use as a qubit. Anharmonicity is found to be reduced by roughly a factor of two compared to conventional metallic junctions, and dependent on gate voltage. Experimental results are consistent with a theoretical model, indicating that Josephson coupling is mediated by a small number of highly transmitting modes in the semiconductor junction.
A. Kringhøj, L. Casparis, M. Hell, T. W. Larsen, F. Kuemmeth, M. Leijnse, K. Flensberg, P. Krogstrup, J. Nygård, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. B 97, 060508 (2018) [pdf] DOI: 10.1103/PhysRevB.97.060508

Supercurrent in a Double Quantum Dot 
Abstract
 2017

ZeroEnergy Modes from Coalescing Andreev States in a TwoDimensional SemiconductorSuperconductor Hybrid Platform 
Abstract
 We investigate zerobias conductance peaks that arise from coalescing subgap Andreev states, consistent with emerging Majorana zero modes, in hybrid semiconductorsuperconductor wires defined in a twodimensional InAs/Al heterostructure using topdown lithography and gating. The measurements indicate a hard superconducting gap, ballistic tunneling contact, and inplane critical fields up to $3$~T. Topdown lithography allows complex geometries, branched structures, and straightforward scaling to multicomponent devices compared to structures made from assembled nanowires.
Henri J. Suominen, Morten Kjaergaard, Alexander R. Hamilton, Javad Shabani, Chris J. Palmstrøm, Charles M. Marcus, Fabrizio Nichele Journal reference: Phys. Rev. Lett. 119, 176805 (2017) [pdf] DOI: 10.1103/PhysRevLett.119.176805

Scaling of Majorana ZeroBias Conductance Peaks 
Abstract
 We report an experimental study of the scaling of zerobias conductance peaks compatible with Majorana zero modes as a function of magnetic field, tunnel coupling, and temperature in onedimensional structures fabricated from an epitaxial semiconductorsuperconductor heterostructure. Results are consistent with theory, including a peak conductance that is proportional to tunnel coupling, saturates at $2e^2/h$, decreases as expected with fielddependent gap, and collapses onto a simple scaling function in the dimensionless ratio of temperature and tunnel coupling.
Fabrizio Nichele, Asbjorn C. C. Drachmann, Alexander M. Whiticar, Eoin C. T. O'Farrell, Henri J. Suominen, Antonio Fornieri, Tian Wang, Geoffrey C. Gardner, Candice Thomas, Anthony T. Hatke, Peter Krogstrup, Michael J. Manfra, Karsten Flensberg, Charles M. Marcus Journal reference: Phys. Rev. Lett. 119, 136803 (2017) [pdf] DOI: 10.1103/PhysRevLett.119.136803

Scalable designs for quasiparticlepoisoningprotected topological quantum computation with Majorana zero modes 
Abstract
 We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurementonly protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological $T$junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.
Torsten Karzig, Christina Knapp, Roman M. Lutchyn, Parsa Bonderson, Matthew B. Hastings, Chetan Nayak, Jason Alicea, Karsten Flensberg, Stephan Plugge, Yuval Oreg, Charles M. Marcus, Michael H. Freedman Journal reference: Phys. Rev. B 95, 235305 (2017) [pdf] DOI: 10.1103/PhysRevB.95.235305

Noise suppression and longrange exchange coupling for gallium arsenide
spin qubits 
Abstract
 This thesis presents the results of the experimental study performed on spin qubits realized in gatedefined gallium arsenide quantum dots, with the focus on noise suppression and longdistance coupling.
 1706.03771v1 [pdf]
Filip Kazimierz Malinowski [pdf]

Conductance spectroscopy on Majorana wires and the inverse proximity effect 
Abstract
 Recent experimental searches for signatures of Majoranalike excitations in proximitized semiconducting nanowires involve conductance spectroscopy, where the evidence sought after is a robust zerobias peak (in longer wires) and its characteristic fielddependent splitting (in shorter wires). Although experimental results partially confirm the theoretical predictions, commonly observed discrepancies still include (i) a zerobias peak that is significantly lower than the predicted value of $2e^2/h$ and (ii) the absence of the expected "Majorana oscillations" of the lowestenergy modes at higher magnetic fields. Here, we investigate how the inevitable presence of a normal drain lead connected to the hybrid wire can affect the conductance spectrum of the hybrid wire. We present numerical results using a oneband model for the proximitized nanowire, where the superconductor is considered to be in the diffusive regime, described by semiclassical Green functions. We show how the presence of the normal drain could (at least partially) account for the observed discrepancies, and we complement this with analytic results providing more insights in the underlying physics.
Jeroen Danon, Esben Bork Hansen, Karsten Flensberg Journal reference: Phys. Rev. B 96, 125420 (2017) [pdf] DOI: 10.1103/PhysRevB.96.125420

Negative Spin Exchange in a Multielectron Quantum Dot 
Abstract
 By operating a oneelectron quantum dot (fabricated between a multielectron dot and a oneelectron reference dot) as a spectroscopic probe, we study the spin properties of a gatecontrolled multielectron GaAs quantum dot at the transition between odd and even occupation number. We observe that the multielectron groundstate transitions from spin1/2like to singletlike to tripletlike as we increase the detuning towards the next higher charge state. The sign reversal in the inferred exchange energy persists at zero magnetic field, and the exchange strength is tunable by gate voltages and inplane magnetic fields. Complementing spin leakage spectroscopy data, the inspection of coherent multielectron spin exchange oscillations provides further evidence for the sign reversal and, inferentially, for the importance of nontrivial multielectron spin exchange correlations.
Frederico Martins, Filip K. Malinowski, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. Lett. 119, 227701 (2017) [pdf] DOI: 10.1103/PhysRevLett.119.227701

Nematic Bond Theory of Heisenberg Helimagnets 
Abstract
 We study classical twodimensional frustrated Heisenberg models with generically incommensurate groundstates. A new theory for the spinnematic "order by disorder" transition is developed based on the selfconsistent determination of the effective exchange coupling bonds. In our approach, fluctuations of the constraint field imposing conservation of the local magnetic moment drive nematicity at low temperatures. The critical temperature is found to be highly sensitive to the peak helimagnetic wavevector, and vanishes continuously when approaching rotation symmetric Lifshitz points. Transitions between symmetry distinct nematic orders may occur by tuning the exchange parameters, leading to lines of bicritical points.
Michael Schecter, Olav. F. Syljuåsen, J. Paaske Journal reference: Phys. Rev. Lett. 119, 157202 (2017) [pdf] DOI: 10.1103/PhysRevLett.119.157202

Kondo blockade due to quantum interference in singlemolecule junctions 
Abstract
 Molecular electronics offers unique scientific and technological possibilities, resulting from both the nanometre scale of the devices and their reproducible chemical complexity. Two fundamental yet different effects, with no classical analogue, have been demonstrated experimentally in singlemolecule junctions: quantum interference due to competing electron transport pathways, and the Kondo effect due to entanglement from strong electronic interactions. Here we unify these phenomena, showing that transport through a spindegenerate molecule can be either enhanced or blocked by Kondo correlations, depending on molecular structure, contacting geometry and applied gate voltages. An exact framework is developed, in terms of which the quantum interference properties of interacting molecular junctions can be systematically studied and understood. We prove that an exact Kondomediated conductance node results from destructive interference in exchangecotunneling. Nonstandard temperature dependences and gatetunable conductance peaks/nodes are demonstrated for prototypical molecular junctions, illustrating the intricate interplay of quantum effects beyond the singleorbital paradigm.
Andrew K. Mitchell, Kim G. L. Pedersen, Per Hedegaard, Jens Paaske Journal reference: Nature Communications, 8, 15210 (2017) [pdf] DOI: 10.1038/ncomms15210

Spectrum of the Nuclear Environment for GaAs Spin Qubits 
Abstract
 Using a singlettriplet spin qubit as a sensitive spectrometer of the GaAs nuclear spin bath, we demonstrate that the spectrum of Overhauser noise agrees with a classical spin diffusion model over six orders of magnitude in frequency, from 1 mHz to 1 kHz, is flat below 10 mHz, and falls as $1/f^2$ for frequency $f \! \gtrsim \! 1$ Hz. Increasing the applied magnetic field from 0.1 T to 0.75 T suppresses electronmediated spin diffusion, which decreases spectral content in the $1/f^2$ region and lowers the saturation frequency, each by an order of magnitude, consistent with a numerical model. Spectral content at megahertz frequencies is accessed using dynamical decoupling, which shows a crossover from the fewpulse regime ($\lesssim \! 16$ $\pi$pulses), where transverse Overhauser fluctuations dominate dephasing, to the manypulse regime ($\gtrsim \! 32$ $\pi$pulses), where longitudinal Overhauser fluctuations with a $1/f$ spectrum dominate.
Filip K. Malinowski, Frederico Martins, Łukasz Cywiński, Mark S. Rudner, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. Lett. 118, 177702 (2017) [pdf] DOI: 10.1103/PhysRevLett.118.177702

Coupling and braiding Majorana bound states in networks defined in twodimensional electron gases with proximityinduced superconductivity 
Abstract
 Twodimensional electron gases with strong spinorbit coupling covered by a superconducting layer offer a flexible and potentially scalable platform for Majorana networks. We predict Majorana bound states (MBSs) to appear for experimentally achievable parameters and realistic gate potentials in two designs: either underneath a narrow stripe of a superconducting layer (Sstripes) or where a narrow stripe has been removed from a uniform layer (Nstripes). The coupling of the MBSs can be tuned for both types in a wide range (<1 nev to>10 $\mu$eV) using gates placed adjacent to the stripes. For both types, we numerically compute the local density of states for two parallel Majoranastripe ends as well as Majorana trijunctions formed in a tuningfork geometry. The MBS coupling between parallel Majorana stripes can be suppressed below 1 neV for potential barriers in the meV range for separations of about 200 nm. We further show that the MBS couplings in a trijunction can be gatecontrolled in a range similar to the intrastripe coupling while maintaining a sizable gap to the excited states (tens of $\mu$eV). Altogether, this suggests that braiding can carried out on a time scale of 10100 ns.
Michael Hell, Karsten Flensberg, Martin Leijnse Journal reference: Phys. Rev. B 96, 035444 (2017) [pdf] DOI: 10.1103/PhysRevB.96.035444

Magnetoelectric coupling in superconductorhelimagnet heterostructures 
Abstract
 The GinzburgLandau free energy of a conventional superconductor coupled to a helimagnet is microscopically derived using functional field integral techniques. We show that the spin texture leads to a Lifshitz invariant in the free energy, which couples the momentum density of the superconducting condensate to the magnetization of the helimagnet. For helimagnets with a conical texture, the Lifshitz invariant yields a spatial modulation of the superconducting phase along the helical wavevector of the magnetic texture. Based on selfconsistent numerical calculations, we verify the theoretical formalism by investigating a superconductor that contains a helical YuShibaRusinov (YSR) chain. We demonstrate that the textureinduced magnetoelectric coupling produces a strong supercurrent along the YSR chain, which induces a detectable magnetic field.
Kjetil M. D. Hals Journal reference: Phys. Rev. B 95, 134504 (2017) [pdf] DOI: 10.1103/PhysRevB.95.134504

Symmetric operation of the resonant exchange qubit 
Abstract
 We operate a resonant exchange qubit in a highly symmetric tripledot configuration using IQmodulated RF pulses. At the resulting threedimensional sweet spot the qubit splitting is an order of magnitude less sensitive to all relevant control voltages, compared to the conventional operating point, but we observe no significant improvement in the quality of Rabi oscillations. For weak driving this is consistent with Overhauser field fluctuations modulating the qubit splitting. For strong driving we infer that effective voltage noise modulates the coupling strength between RF drive and the qubit, thereby quickening Rabi decay. Application of CPMG dynamical decoupling sequences consisting of up to n = 32 {\pi} pulses significantly prolongs qubit coherence, leading to marginally longer dephasing times in the symmetric configuration. This is consistent with dynamical decoupling from low frequency noise, but quantitatively cannot be explained by effective gate voltage noise and Overhauser field fluctuations alone. Our results inform recent strategies for the utilization of partial sweet spots in the operation and longdistance coupling of tripledot qubits.
Filip K. Malinowski, Frederico Martins, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. B 96, 045443 (2017) [pdf] DOI: 10.1103/PhysRevB.96.045443

Notch filtering the nuclear environment of a spin qubit 
Abstract
 Electron spins in gatedefined quantum dots provide a promising platform for quantum computation. In particular, spinbased quantum computing in gallium arsenide takes advantage of the high quality of semiconducting materials, reliability in fabricating arrays of quantum dots, and accurate qubit operations. However, the effective magnetic noise arising from the hyperfine interaction with uncontrolled nuclear spins in the host lattice constitutes a major source of decoherence. Low frequency nuclear noise, responsible for fast (10 ns) inhomogeneous dephasing, can be removed by echo techniques. High frequency nuclear noise, recently studied via echo revivals, occurs in narrow frequency bands related to differences in Larmor precession of the three isotopes $\mathbf{^{69}Ga}$, $\mathbf{^{71}Ga}$, and $\mathbf{^{75}As}$. Here we show that both low and high frequency nuclear noise can be filtered by appropriate dynamical decoupling sequences, resulting in a substantial enhancement of spin qubit coherence times. Using nuclear notch filtering, we demonstrate a spin coherence time ($\mathbf{T_{2}}$) of 0.87 ms, five orders of magnitude longer than typical exchange gate times, and exceeding the longest coherence times reported to date in Si/SiGe gatedefined quantum dots.
F. K. Malinowski, F. Martins, P. D. Nissen, E. Barnes, Ł. Cywiński, M. S. Rudner, S. Fallahi, G. C. Gardner, M. J. Manfra, C. M. Marcus, F. Kuemmeth Journal reference: Nat. Nanotechnol. 12, 1620 (2017) [pdf] DOI: 10.1038/nnano.2016.170

Current–phase relations of fewmode InAs nanowire Josephson junctions 
Abstract
 Gatetunable semiconductor nanowires with superconducting leads have great potential for quantum computation and as model systems for mesoscopic Josephson junctions. The supercurrent, $I$, versus the phase, $\phi$, across the junction is called the currentphase relation (CPR). It can reveal not only the amplitude of the critical current, but also the number of modes and their transmission. We measured the CPR of many individual InAs nanowire Josephson junctions, one junction at a time. Both the amplitude and shape of the CPR varied between junctions, with small critical currents and skewed CPRs indicating fewmode junctions with high transmissions. In a gatetunable junction, we found that the CPR varied with gate voltage: Near the onset of supercurrent, we observed behavior consistent with resonant tunneling through a single, highly transmitting mode. The gate dependence is consistent with modeled subband structure that includes an effective tunneling barrier due to an abrupt change in the Fermi level at the boundary of the gatetuned region. These measurements of skewed, tunable, fewmode CPRs are promising both for applications that require anharmonic junctions and for Majorana readout proposals.
Eric M. Spanton, Mingtang Deng, Saulius Vaitiekėnas, Peter Krogstrup, Jesper Nygård, Charles M. Marcus, Kathryn A. Moler Journal reference: Nature Physics (2017) [pdf] DOI: 10.1038/nphys4224

Majorana box qubits 
Abstract
 Quantum information protected by the topology of the storage medium is expected to exhibit long coherence times. Another feature are topologically protected gates generated through braiding of Majorana bound states. However, braiding requires structures with branched topological segments which have inherent difficulties in the semiconductorsuperconductor heterostructures now believed to host Majorana bound states. In this paper, we construct quantum bits taking advantage of the topological protection and nonlocal properties of Majorana bound states in a network of parallel wires, but without relying on braiding for quantum gates. The elementary unit is made from three topological wires, two wires coupled by a trivial superconductor and the third acting as an interference arm. Coulomb blockade of the combined wires spawns a fractionalized spin, nonlocally addressable by quantum dots used for singlequbit readout, initialization, and manipulation. We describe how the same tools allow for measurementbased implementation of the Clifford gates, in total making the architecture universal. Proofofprinciple demonstration of topologically protected qubits using existing techniques is therefore within reach.
Stephan Plugge, Asbjørn Rasmussen, Reinhold Egger, Karsten Flensberg Journal reference: New J. Phys 19, 012001 (2017) [pdf] DOI: 10.1088/13672630/aa54e1

Transport Signatures of Quasiparticle Poisoning in a Majorana Island 
Abstract
 We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normalmetal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (~ 1 {\mu}s) and sets a bound for a weakly coupled island (> 10 {\mu}s). Fluctuations in the gatevoltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. In energy units, fluctuations are consistent with previous measurements.
S. M. Albrecht, E. B. Hansen, A. P. Higginbotham, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, J. Danon, K. Flensberg, C. M. Marcus Journal reference: Phys. Rev. Lett. 118, 137701 (2017) [pdf] DOI: 10.1103/PhysRevLett.118.137701

TwoDimensional Platform for Networks of Majorana Bound States 
Abstract
 We model theoretically a twodimensional electron gas (2DEG) covered by a superconductor and demonstrate that topological superconducting channels are formed when stripes of the superconducting layer are removed. As a consequence, Majorana bound states (MBS) are created at the ends of the stripes. We calculate the topological invariant and energy gap of a single stripe, using realistic values for an InAs 2DEG proximitized by an epitaxial Al layer. We show that the topological gap is enhanced when the structure is made asymmetric. This can be achieved by either imposing a phase difference (by driving a supercurrent or using a magneticflux loop) over the strip or by replacing one superconductor by a metallic gate. Both strategies also enable control over the MBS splitting, thereby facilitating braiding and readout schemes based on controlled fusion of MBS. Finally, we outline how a network of Majorana stripes can be designed.
Michael Hell, Martin Leijnse, Karsten Flensberg Journal reference: Phys. Rev. Lett. 118, 107701 (2017) [pdf] DOI: 10.1103/PhysRevLett.118.107701

Proximity Effect Transfer from NbTi into a Semiconductor Heterostructure via Epitaxial Aluminum 
Abstract
 We demonstrate the transfer of the superconducting properties of NbTia largegap highcriticalfield superconductorinto an InAs heterostructure via a thin intermediate layer of epitaxial Al. Two device geometries, a Josephson junction and a gatedefined quantum point contact, are used to characterize interface transparency and the twostep proximity effect. In the Josephson junction, multiple Andreev reflection reveal nearunity transparency, with an induced gap $\Delta^*=0.50~\mathrm{meV}$ and a critical temperature of $7.8~\mathrm{K}$. Tunneling spectroscopy yields a hard induced gap in the InAs adjacent to the superconductor of $\Delta^*=0.43~\mathrm{meV}$ with substructure characteristic of both Al and NbTi.
A. C. C. Drachmann, H. J. Suominen, M. Kjaergaard, B. Shojaei, C. J. Palmstrøm, C. M. Marcus, F. Nichele Journal reference: Nano Lett. 17, 1200 (2017) [pdf] DOI: 10.1021/acs.nanolett.6b04964

Giant SpinOrbit Splitting in Inverted

Abstract
 Transport measurements in inverted InAs/GaSb quantum wells reveal a giant spinorbit splitting of the energy bands close to the hybridization gap. The splitting results from the interplay of electronhole mixing and spinorbit coupling, and can exceed the hybridization gap. We experimentally investigate the band splitting as a function of top gate voltage for both electronlike and holelike states. Unlike conventional, noninverted twodimensional electron gases, the Fermi energy in InAs/GaSb can cross a single spinresolved band, resulting in full spinorbit polarization. In the fully polarized regime we observe exotic transport phenomena such as quantum Hall plateaus evolving in $e^2/h$ steps and a nontrivial Berry phase.
Fabrizio Nichele, Morten Kjaergaard, Henri J. Suominen, Rafal Skolasinski, Michael Wimmer, BinhMinh Nguyen, Andrey A. Kiselev, Wei Yi, Marko Sokolich, Michael J. Manfra, Fanming Qu, Arjan J. A. Beukman, Leo P. Kouwenhoven, Charles M. Marcus Journal reference: Phys. Rev. Lett. 118, 016801 (2017) [pdf] DOI: 10.1103/PhysRevLett.118.016801

Anomalous Fraunhofer interference in epitaxial superconductorsemiconductor Josephson junctions 
Abstract
 We investigate patterns of critical current as a function of perpendicular and inplane magnetic fields in superconductorsemiconductorsuperconductor (SNS) junctions based on InAs/InGaAs heterostructures with an epitaxial Al layer. This material system is of interest due to its exceptionally good superconductorsemiconductor coupling, as well as large spinorbit interaction and gfactor in the semiconductor. Thin epitaxial Al allows the application of large inplane field without destroying superconductivity. For fields perpendicular to the junction, flux focusing results in aperiodic node spacings in the pattern of critical currents known as Fraunhofer patterns by analogy to the related interference effect in optics. Adding an inplane field yields two further anomalies in the pattern. First, higher order nodes are systematically strengthened, indicating current flow along the edges of the device, as a result of confinement of Andreev states driven by an induced flux dipole; second, asymmetries in the interference appear that depend on the field direction and magnitude. A model is presented, showing good agreement with experiment, elucidating the roles of flux focusing, Zeeman and spinorbit coupling, and disorder in producing these effects.
H. J. Suominen, J. Danon, M. Kjaergaard, K. Flensberg, J. Shabani, C. J. Palmstrøm, F. Nichele, C. M. Marcus Journal reference: Phys. Rev. B 95, 035307 (2017) [pdf] DOI: 10.1103/PhysRevB.95.035307

Transparent SemiconductorSuperconductor Interface and Induced Gap in an Epitaxial Heterostructure Josephson Junction 
Abstract
 Measurement of multiple Andreev reflection (MAR) in a Josephson junction made from an InAs heterostructure with epitaxial aluminum is used to quantify the highly transparent semiconductorsuperconductor interface, indicating nearunity transmission. The observed temperature dependence of MAR does not follow a conventional BCS form, but instead agrees with a model in which the density of states in the quantum well acquires an effective induced gap, in our case 180 {\mu}eV, close to that of the epitaxial superconductor. Carrier density dependence of MAR is investigated using a depletion gate, revealing the subband structure of the semiconductor quantum well, consistent with magnetotransport experiment of the bare InAs performed on the same wafer.
M. Kjaergaard, H. J. Suominen, M. P. Nowak, A. R. Akhmerov, J. Shabani, C. J. Palmstrøm, F. Nichele, C. M. Marcus Journal reference: Phys. Rev. Applied 7, 034029 (2017) [pdf] DOI: 10.1103/PhysRevApplied.7.034029

Normal, superconducting and topological regimes of hybrid double quantum dots 
Abstract
 Epitaxial semiconductorsuperconductor hybrid materials are an excellent basis for studying mesoscopic and topological superconductivity, as the semiconductor inherits a hard superconducting gap while retaining tunable carrier density. Here, we investigate doublequantumdot devices made from InAs nanowires with a patterned epitaxial Al twofacet shell that proximitizes two gatedefined segments along the nanowire. We follow the evolution of mesoscopic superconductivity and charging energy in this system as a function of magnetic field and voltagetuned barriers. Interdot coupling is varied from strong to weak using side gates, and the ground state is varied between normal, superconducting, and topological regimes by applying a magnetic field. We identify the topological transition by tracking the spacing between successive cotunneling peaks as a function of axial magnetic field and show that the individual dots host weakly hybridized Majorana modes.
D. Sherman, J. S. Yodh, S. M. Albrecht, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Nature Nanotechnology 12, 212 (2017) [pdf] DOI: 10.1038/nnano.2016.227

ZeroEnergy Modes from Coalescing Andreev States in a TwoDimensional SemiconductorSuperconductor Hybrid Platform 
Abstract
 2016

Majorana bound state in a coupled quantumdot hybridnanowire system 
Abstract
 Hybrid nanowires combining semiconductor and superconductor materials appear well suited for the creation, detection, and control of Majorana bound states (MBSs). We demonstrate the emergence of MBSs from coalescing Andreev bound states (ABSs) in a hybrid InAs nanowire with epitaxial Al, using a quantum dot at the end of the nanowire as a spectrometer. Electrostatic gating tuned the nanowire density to a regime of one or a few ABSs. In an applied axial magnetic field, a topological phase emerges in which ABSs move to zero energy and remain there, forming MBSs. We observed hybridization of the MBS with the enddot bound state, which is in agreement with a numerical model. The ABS/MBS spectra provide parameters that are useful for understanding topological superconductivity in this system.
M. T. Deng, S. Vaitiekenas, E. B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Science 354, 15571562 (2016) [pdf] DOI: 10.1126/science.aaf3961

Quantized conductance doubling and hard gap in a twodimensional semiconductor–superconductor heterostructure 
Abstract
 The prospect of coupling a twodimensional (2D) semiconductor heterostructure to a superconductor opens new research and technology opportunities, including fundamental problems in mesoscopic superconductivity, scalable superconducting electronics, and new topological states of matter. For instance, one route toward realizing topological matter is by coupling a 2D electron gas (2DEG) with strong spinorbit interaction to an swave superconductor. Previous efforts along these lines have been hindered by interface disorder and unstable gating. Here, we report measurements on a gateable InGaAs/InAs 2DEG with patterned epitaxial Al, yielding multilayer devices with atomically pristine interfaces between semiconductor and superconductor. Using surface gates to form a quantum point contact (QPC), we find a hard superconducting gap in the tunneling regime, overcoming the softgap problem in 2D superconductorsemiconductor hybrid systems. With the QPC in the open regime, we observe a first conductance plateau at 4e^2/h, as expected theoretically for a normalQPCsuperconductor structure. The realization of a hardgap semiconductorsuperconductor system that is amenable to topdown processing provides a means of fabricating scalable multicomponent hybrid systems for applications in lowdissipation electronics and topological quantum information.
M. Kjaergaard, F. Nichele, H. J. Suominen, M. P. Nowak, M. Wimmer, A. R. Akhmerov, J. A. Folk, K. Flensberg, J. Shabani, C. J. Palmstrom, C. M. Marcus Journal reference: Nat. Commun. 7, 12841 (2016) [pdf] DOI: 10.1038/ncomms12841

InAs Nanowire with Epitaxial Aluminum as a SingleElectron Transistor with Fixed Tunnel Barriers 
Abstract
 We report on fabrication of singleelectron transistors using InAs nanowires with epitaxial aluminium with fixed tunnel barriers made of aluminium oxide. The devices exhibit a hard superconducting gap induced by the proximized aluminium cover shell and they behave as metallic singleelectron transistors. In contrast to the typical few channel contacts in semiconducting devices, our approach forms opaque multichannel contacts to a semiconducting wire and thus provides a complementary way to study them. In addition, we confirm that unwanted extra quantum dots can appear at the surface of the nanowire. Their presence is prevented in our devices, and also by inserting a protective layer of GaAs between the InAs and Al, the latter being suitable for standard measurement methods.
M. Taupin, E. Mannila, P. Krogstrup, V. F. Maisi, H. Nguyen, S. M. Albrecht, J. Nygard, C. M. Marcus, J. P. Pekola Journal reference: Phys. Rev. Applied 6, 054017 (2016) [pdf] DOI: 10.1103/PhysRevApplied.6.054017

Localization lifetime of a many‐body system with periodic constructed disorder 
Abstract
 We show that, in a manybody system, all particles can be strongly confined to the initially occupied sites for a time that scales as a high power of the ratio of the bandwidth of site energies to the hopping amplitude. Such timedomain formulation is complementary to the formulation of the manybody localization of all stationary states with a large localization length. The long localization lifetime is achieved by constructing a periodic sequence of site energies with a large period in a onedimensional chain. The scaling of the localization lifetime is independent of the number of particles for a broad range of the coupling strength. The analytical results are confirmed by numerical calculations.
M. Schecter, M. Shapiro, M. I. Dykman [pdf] DOI: 10.1002/andp.201600366 1611.05713v1 [pdf]

Tunable Magnetic Anisotropy from HigherHarmonics Exchange Scattering on the Surface of a Topological Insulator 
Abstract
 We show that higherharmonics exchange scattering from a magnetic adatom on the surface of a three dimensional topological insulator leads to a magnetic anisotropy whose magnitude and sign may be tuned by adjusting the chemical potential of the helical surface band. As chemical potential moves from the Dirac point towards the surface band edge, the surface normal is found to change from magnetic easy, to hard axis. Hexagonal warping is shown to diminish the region with easy axis anisotropy, and to suppress the anisotropy altogether. This indirect contribution can be comparable in magnitude to the intrinsic term arising from crystal field splitting and atomic spinorbit coupling, and its tunability with chemical potential makes the two contributions experimentally discernible, and endows this source of anisotropy with potentially interesting magnetic functionality.
Jens Paaske, Erikas Gaidamauskas Journal reference: Phys. Rev. Lett. 117, 177201 (2016) [pdf] DOI: 10.1103/PhysRevLett.117.177201

Spiral magnetic order and topological superconductivity in a chain of magnetic adatoms on a twodimensional superconductor 
Abstract
 We study the magnetic and electronic phases of a 1D magnetic adatom chain on a 2D superconductor. In particular, we confirm the existence of a `selforganized' 1D topologically nontrivial superconducting phase within the set of subgap YuShibaRusinov (YSR) states formed along the magnetic chain. This phase is stabilized by incommensurate spiral correlations within the magnetic chain that arise from the competition between shortrange ferromagnetic and longrange antiferromagnetic electroninduced exchange interactions, similar to a recent study for a 3D superconductor [M. Schecter et al. Phys. Rev. B 93, 140503(R) 2016]. The exchange interaction along diagonal directions are also considered and found to display behavior similar to a 1D substrate when close to half filling. We show that the topological phase diagram is robust against local superconducting order parameter suppression and weak substrate spinorbit coupling. Lastly, we study the effect of a direct ferromagnetic exchange coupling between the adatoms, and find the region of spiral order in the phase diagram to be significantly enlarged in a wide range of the direct exchange coupling.
M. H. Christensen, M. Schecter, K. Flensberg, B. M. Andersen, J. Paaske Journal reference: Phys. Rev. B 94, 144509 (2016) [pdf] DOI: 10.1103/PhysRevB.94.144509

Nogo theorem for a timereversal invariant topological phase in noninteracting systems coupled to conventional superconductors 
Abstract
 We prove that a system of noninteracting electrons proximity coupled to a conventional swave superconductor cannot realize a time reversal invariant topological phase. This is done by showing that for such a system, in either one or two dimensions, the topological invariant of the corresponding symmetry class (DIII) is always trivial. Our results suggest that the pursuit of Majorana bound states in timereversal invariant systems should be aimed at interacting systems or at proximity to unconventional superconductors.
Arbel Haim, Erez Berg, Karsten Flensberg, Yuval Oreg Journal reference: Phys. Rev. B 94, 161110 (2016) [pdf] DOI: 10.1103/PhysRevB.94.161110

Interactiondriven topological superconductivity in one dimension 
Abstract
 We study onedimensional topological superconductivity in the presence of timereversal symmetry. This phase is characterized by having a bulk gap, while supporting a Kramers' pair of zeroenergy Majorana bound states at each of its ends. We present a general simple model which is driven into this topological phase in the presence of repulsive electronelectron interactions. We further propose two experimental setups and show that they realize this model at low energies. The first setup is a narrow twodimensional topological insulator partially covered by a conventional swave superconductor, and the second is a semiconductor wire in proximity to an swave superconductor. These systems can therefore be used to realize and probe the timereversal invariant topological superconducting phase. The effect of interactions is studied using both a meanfield approach and a renormalization group analysis.
Arbel Haim, Konrad Wölms, Erez Berg, Yuval Oreg, Karsten Flensberg Journal reference: Phys. Rev. B 94, 115124 (2016) [pdf] DOI: 10.1103/PhysRevB.94.115124

Signatures of Majorana Kramers pairs in superconductorLuttinger liquid and superconductorquantum dotnormal lead junctions 
Abstract
 Timereversal invariant topological superconductors are characterized by the presence of Majorana Kramers pairs localized at defects. One of the transport signatures of Majorana Kramers pairs is the quantized differential conductance of $4e^2/h$ when such a onedimensional superconductor is coupled to a normalmetal lead. The resonant Andreev reflection, responsible for this phenomenon, can be understood as the boundary condition change for lead electrons at low energies. In this paper, we study the stability of the Andreev reflection fixed point with respect to electronelectron interactions in the Luttinger liquid. We first calculate the phase diagram for the Luttinger liquidMajorana Kramers pair junction and show that its lowenergy properties are determined by Andreev reflection scattering processes in the spintriplet channel, i.e. the corresponding Andreev boundary conditions are similar to that in a spintriplet superconductor  normal lead junction. We also study here a quantum dot coupled to a normal lead and a Majorana Kramers pair and investigate the effect of local repulsive interactions leading to an interplay between Kondo and Majorana correlations. Using a combination of renormalization group analysis and slaveboson meanfield theory, we show that the system flows to a new fixed point which is controlled by the Majorana interaction rather than the Kondo coupling. This Majorana fixed point is characterized by correlations between the localized spin and the fermion parity of each spin sector of the topological superconductor. We investigate the stability of the Majorana phase with respect to Gaussian fluctuations.
Younghyun Kim, Dong E. Liu, Erikas Gaidamauskas, Jens Paaske, Karsten Flensberg, Roman M. Lutchyn Journal reference: Phys. Rev. B 94, 075439 (2016) [pdf] DOI: 10.1103/PhysRevB.94.075439

Quantization of Hall Resistance at the Metallic Interface between an Oxide Insulator and

Abstract
 The twodimensional metal forming at the interface between an oxide insulator and SrTiO3 provides new opportunities for oxide electronics. However, the quantum Hall effect, one of the most fascinating effects of electrons confined in two dimensions, remains underexplored at these complex oxide heterointerfaces. Here, we report the experimental observation of quantized Hall resistance in a SrTiO3 heterointerface based on the modulationdoped amorphousLaAlO$_{3}$/SrTiO$_{3}$ heterostructure, which exhibits both high electron mobility exceeding 10000 cm$^{2}$/Vs and low carrier density on the order of ~10$^{12}$ cm$^{2}$. Along with unambiguous Shubnikovde Haas oscillations, the spacing of the quantized Hall resistance suggests that the interface is comprised of a single quantum well with ten parallel conducting twodimensional subbands. This provides new insight into the electronic structure of conducting oxide interfaces and represents an important step towards designing and understanding advanced oxide devices.
Felix Trier, Guenevere E. D. K. Prawiroatmodjo, Zhicheng Zhong, Merlin von Soosten, Dennis Valbjørn Christensen, Arghya Bhowmik, Juan Maria García Lastra, Yunzhong Chen, Thomas Sand Jespersen, Nini Pryds Journal reference: Phys. Rev. Lett. 117, 096804 (2016) [pdf] DOI: 10.1103/PhysRevLett.117.096804

Edge transport in the trivial phase of InAs/GaSb 
Abstract
 We present transport and scanning SQUID measurements on InAs/GaSb double quantum wells, a system predicted to be a twodimensional topological insulator. Top and back gates allow independent control of density and band offset, allowing tuning from the trivial to the topological regime. In the trivial regime, bulk conductivity is quenched but transport persists along the edges, superficially resembling the predicted helical edgechannels in the topological regime. We characterize edge conduction in the trivial regime in a wide variety of sample geometries and measurement configurations, as a function of temperature, magnetic field, and edge length. Despite similarities to studies claiming measurements of helical edge channels, our characterization points to a nontopological origin for these observations.
Fabrizio Nichele, Henri J. Suominen, Morten Kjaergaard, Charles M. Marcus, Ebrahim Sajadi, Joshua A. Folk, Fanming Qu, Arjan J. A. Beukman, Folkert K. de Vries, Jasper van Veen, Stevan NadjPerge, Leo P. Kouwenhoven, BinhMinh Nguyen, Andrey A. Kiselev, Wei Yi, Marko Sokolich, Michael J. Manfra, Eric M. Spanton, Kathryn A. Moler Journal reference: New J. Phys. 18, 083005 (2016) [pdf] DOI: 10.1088/13672630/18/8/083005

Composite Topological Excitations in FerromagnetSuperconductor Heterostructures 
Abstract
 We investigate the formation of a new type of composite topological excitation  the skyrmionvortex pair (SVP)  in hybrid systems consisting of coupled ferromagnetic and superconducting layers. Spinorbit interaction in the superconductor mediates a magnetoelectric coupling between the vortex and the skyrmion, with a sign (attractive or repulsive) that depends on the topological indices of the constituents. We determine the conditions under which a bound SVP is formed, and characterize the range and depth of the effective binding potential through analytical estimates and numerical simulations. Furthermore, we develop a semiclassical description of the coupled skyrmionvortex dynamics and discuss how SVPs can be controlled by applied spin currents.
Kjetil M. D. Hals, Michael Schecter, Mark S. Rudner Journal reference: Phys. Rev. Lett. 117, 017001 (2016) [pdf] DOI: 10.1103/PhysRevLett.117.017001

Supercurrentinduced spinorbit torques 
Abstract
 We theoretically investigate the supercurrentinduced magnetization dynamics of a twodimensional lattice of ferromagnetically ordered spins placed on a conventional superconductor with broken spatial inversion symmetry and strong spinorbit coupling. We develop a phenomenological description of the coupled dynamics of the superconducting condensate and the spin system, and demonstrate that supercurrents produce a reactive spinorbit torque on the magnetization. By performing a microscopic selfconsistent calculation, we show that the spinorbit torque originates from a spinpolarization of the Cooper pairs due to currentinduced spintriplet correlations. Interestingly, we find that there exists an intrinsic limitation for the maximum achievable spinorbit torque, which is determined by the coupling strength between the condensate and the spin system. In proximitized holedoped semiconductors, the maximum achievable spinorbit torque field is estimated to be on the order of $0.16$ mT, which is comparable to the critical field for currentinduced magnetization switching in ferromagnetic semiconductors.
Kjetil M. D. Hals Journal reference: Phys. Rev. B 93, 115431 (2016) [pdf] DOI: 10.1103/PhysRevB.93.115431

Roadmap to Majorana surface codes 
Abstract
 Surface codes offer a very promising avenue towards faulttolerant quantum computation. We argue that twodimensional interacting networks of Majorana bound states in topological superconductor/semiconductor heterostructures hold several distinct advantages in that direction, both concerning the hardware realization and the actual operation of the code. We here discuss how topologically protected logical qubits in this Majorana surface code architecture can be defined, initialized, manipulated, and read out. All physical ingredients needed to implement these operations are routinely used in topologically trivial quantum devices. In particular, we show that by means of quantum interference terms in linear conductance measurements, composite singleelectron pumping protocols, and gatetunable tunnel barriers, the full set of quantum gates required for universal quantum computation can be implemented.
S. Plugge, L. A. Landau, E. Sela, A. Altland, K. Flensberg, R. Egger Journal reference: Phys. Rev. B 94, 174514 (2016) [pdf] DOI: 10.1103/PhysRevB.94.174514

Quantum charge fluctuations of a proximitized nanowire 
Abstract
 Motivated by recent experiment, we consider charging of a nanowire which is proximitized by a superconductor and connected to a normalstate lead by a singlechannel junction. The charge $Q$ of the nanowire is controlled by gate voltage $e{\cal N}_g/C$. A finite conductance of the contact allows for quantum charge fluctuations, making the function $Q(\mathcal{N}_g)$ continuous. It depends on the relation between the superconducting gap $\Delta$ and the effective charging energy $E^*_C$. The latter is determined by the junction conductance, in addition to the geometrical capacitance of the proximitized nanowire. We investigate $Q(\mathcal{N}_g)$ at zero magnetic field $B$, and at fields exceeding the critical value $B_c$ corresponding to the topological phase transition. Unlike the case of $\Delta = 0$, the function $Q(\mathcal{N}_g)$ is analytic even in the limit of negligible level spacing in the nanowire. At $B=0$ and $\Delta>E^*_C$, the maxima of $dQ/d\mathcal{N}_g$ are smeared by $2e$fluctuations described by a singlechannel "charge Kondo" physics, while the $B=0$, $\Delta<e^*_c$ case="case" is="is" described="described" by="by" a="a" crossover="crossover" between="between" the="the" kondo="Kondo" and="and" mixedvalence="mixedvalence" regimes="regimes" of="of" the="the" anderson="Anderson" impurity="impurity" model.="model." in="In" the="the" topological="topological" phase,="phase," $q(\mathcal{n}_g)$="$Q(\mathcal{N}_g)$" is="is" analytic="analytic" function="function" of="of" the="the" gate="gate" voltage="voltage" with="with" $e$periodic="$e$periodic" steps.="steps." in="In" the="the" weak="weak" tunneling="tunneling" limit,="limit," $dq/d\mathcal{n}_g$="$dQ/d\mathcal{N}_g$" has="has" peaks="peaks" corresponding="corresponding" to="to" breitwigner="BreitWigner" resonances,="resonances," whereas="whereas" in="In" the="the" strong="strong" tunneling="tunneling" limit="limit" (i.e.,="(i.e.," small="small" reflection="reflection" amplitude="amplitude" $r$="$r$" )=")" these="these" resonances="resonances" are="are" broadened,="broadened," and="and" $dq/d\mathcal{n}_ge="$dQ/d\mathcal{N}_ge" \propto="\propto" r\cos(2\pi="r\cos(2\pi" \mathcal{n}_g)$.
Roman M. Lutchyn, Karsten Flensberg, Leonid I. Glazman Journal reference: Phys. Rev. B 94, 125407 (2016) [pdf] DOI: 10.1103/PhysRevB.94.125407

Noncollinear SpinOrbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot 
Abstract
 We demonstrate experimentally that noncollinear intrinsic spinorbit magnetic fields can be realized in a curved carbon nanotube twosegment device. Each segment, analyzed in the quantum dot regime, shows near fourfold degenerate shell structure allowing for identification of the spinorbit coupling and the angle between the two segments. Furthermore, we determine the four unique spin directions of the quantum states for specific shells and magnetic fields. This class of quantum dot systems is particularly interesting when combined with induced superconducting correlations as it may facilitate unconventional superconductivity and detection of Cooper pair entanglement. Our device comprises the necessary elements.
Morten Canth Hels, Bernd Braunecker, Kasper GroveRasmussen, Jesper Nygård Journal reference: Phys. Rev. Lett. 117, 276802 (2016) [pdf] DOI: 10.1103/PhysRevLett.117.276802

Time scales for Majorana manipulation using Coulomb blockade in gatecontrolled superconducting nanowires 
Abstract
 We numerically compute the lowenergy spectrum of a gatecontrolled superconducting topological nanowire segmented into two islands, each Josephsoncoupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could provide a platform for testing Majorana fusion rules. We analyze the crossover between (i) a chargedominated regime utilizable for initialization and readout of Majorana bound states, (ii) a singleisland regime for dominating interisland Majorana coupling, (iii) a Josephsonplasmon regime for large coupling to the bulk superconductors, and (iv) a regime of four Majorana bound states allowing for topologically protected Majorana manipulations. From the energy spectrum, we derive conservative estimates for the time scales of a fusionrule testing protocol proposed recently [arXiv:1511.05153]. We also analyze the steps needed for basic Majorana braiding operations in branched nanowire structures.
Michael Hell, Jeroen Danon, Karsten Flensberg, Martin Leijnse Journal reference: Phys. Rev. B 94, 035424 (2016) [pdf] DOI: 10.1103/PhysRevB.94.035424

Generic helical edge states due to Rashba spinorbit coupling in a topological insulator 
Abstract
 We study the helical edge states of a twodimensional topological insulator without axial spin symmetry due to the Rashba spinorbit interaction. Lack of axial spin symmetry can lead to socalled generic helical edge states, which have energydependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spinorbit coupling within the BernevigHughesZhang model, for both a single isolated edge and for a finite width ribbon. In the singleedge case, we analytically quantify the energy dependence of the spin orientation, which turns out to be weak for a realistic HgTe quantum well. Nevertheless, finite size effects combined with Rashba spinorbit coupling result in two avoided crossings in the energy dispersions, where the spin orientation variation of the edge states is very significantly increased for realistic parameters. Finally, our analytical results are found to compare well to a numerical tightbinding regularization of the model.
Laura Ortiz, Rafael A. Molina, Gloria Platero, Anders Mathias Lunde Journal reference: Phys. Rev. B 93, 205431 (2016) [pdf] DOI: 10.1103/PhysRevB.93.205431

Survival, decay, and topological protection in nonHermitian quantum
transport 
Abstract
 NonHermitian quantum systems can exhibit unique observables characterizing topologically protected transport in the presence of decay. The topological protection arises from winding numbers associated with nondecaying dark states, which are decoupled from the environment and thus immune to dissipation. Here we develop a classification of topological dynamical phases for onedimensional quantum systems with periodicallyarranged absorbing sites. This is done using the framework of Bloch theory to describe the dark states and associated topological invariants. The observables, such as the average particle displacement over its life span, feature quantized contributions that are governed by the winding numbers of cycles around darkstate submanifolds in the Hamiltonian parameter space. Changes in the winding numbers at topological transitions are manifested in nonanalytic behavior of the observables. We discuss the conditions under which nontrivial topological phases may be found, and provide examples that demonstrate how additional constraints or symmetries can lead to rich topological phase diagrams.
 1605.07652v1 [pdf]
Mark S. Rudner, Michael Levin, Leonid S. Levitov [pdf]

Evidence of weak superconductivity at the roomtemperature grown

Abstract
 The twodimensional electron gas at the crystalline LaAlO$_{3}$/SrTiO$_{3}$ (cLAO/STO) interface has sparked large interest due to its exotic properties including an intriguing gatetunable superconducting phase. While there is growing evidence of pronounced spatial inhomogeneity in the conductivity at STObased interfaces, the consequences for superconductivity remain largely unknown. We study interfaces based on amorphous LAO top layers grown at room temperature (aLAO/STO) and demonstrate a superconducting phase similar to cLAO/STO, however, with a gatetunable critical temperature of $460 \, \mathrm{mK}$, higher than any previously reported values for cLAO/STO. The dependence of the superconducting critical current on temperature, magnetic field and backgatecontrolled doping is found to be consistently described by a model of a random array of Josephsoncoupled superconducting domains.
Guenevere E. D. K. Prawiroatmodjo, Felix Trier, Dennis V. Christensen, Yunzhong Chen, Nini Pryds, Thomas S. Jespersen Journal reference: Phys. Rev. B 93, 184504 (2016) [pdf] DOI: 10.1103/PhysRevB.93.184504

Selforganized topological superconductivity in a YuShibaRusinov chain 
Abstract
 We study a chain of magnetic moments exchange coupled to a conventional three dimensional superconductor. In the normal state the chain orders into a collinear configuration, while in the superconducting phase we find that ferromagnetism is unstable to the formation of a magnetic spiral state. Beyond weak exchange coupling the spiral wavevector greatly exceeds the inverse superconducting coherence length as a result of the strong spinspin interaction mediated through the subgap band of YuShibaRusinov states. Moreover, the simple spinspin exchange description breaks down as the subgap band crosses the Fermi energy, wherein the spiral phase becomes stabilized by the spontaneous opening of a $p$wave superconducting gap within the band. This leads to the possibility of electrondriven topological superconductivity with Majorana boundary modes using magnetic atoms on superconducting surfaces.
M. Schecter, K. Flensberg, M. H. Christensen, B. M. Andersen, J. Paaske Journal reference: Phys. Rev. B 93, 140503 (2016) [pdf] DOI: 10.1103/PhysRevB.93.140503

Milestones Toward MajoranaBased Quantum Computing 
Abstract
 We introduce a scheme for preparation, manipulation, and readout of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantumdot experiments, including gatecontrol of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zeromode detection and quantum computing that includes (1) detection of fusion rules for nonAbelian anyons using either proximal charge sensors or pumped current; (2) validation of a prototype topological qubit; and (3) demonstration of nonAbelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system's excitation gap, quasiparticle poisoning rates, residual Majorana zeromode splittings, and topologicalqubit coherence times. These prebraiding experiments can be adapted to other manipulation and readout schemes as well.
David Aasen, Michael Hell, Ryan V. Mishmash, Andrew Higginbotham, Jeroen Danon, Martin Leijnse, Thomas S. Jespersen, Joshua A. Folk, Charles M. Marcus, Karsten Flensberg, Jason Alicea Journal reference: Phys. Rev. X 6, 031016 (2016) [pdf] DOI: 10.1103/PhysRevX.6.031016

Filter function formalism beyond pure dephasing and nonMarkovian noise in singlettriplet qubits 
Abstract
 The filter function formalism quantitatively describes the dephasing of a qubit by a bath that causes Gaussian fluctuations in the qubit energies with an arbitrary noise power spectrum. Here, we extend this formalism to account for more general types of noise that couple to the qubit through terms that do not commute with the qubit's bare Hamiltonian. Our approach applies to any power spectrum that generates slow noise fluctuations in the qubit's evolution. We demonstrate our formalism in the case of singlettriplet qubits subject to both quasistatic nuclear noise and $1/\omega^\alpha$ charge noise and find good agreement with recent experimental findings. This comparison shows the efficacy of our approach in describing real systems and additionally highlights the challenges with distinguishing different types of noise in free induction decay experiments.
Edwin Barnes, Mark S. Rudner, Frederico Martins, Filip K. Malinowski, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. B 93, 121407 (2016) [pdf] DOI: 10.1103/PhysRevB.93.121407

Exponential protection of zero modes in Majorana islands 
Abstract
 Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of faulttolerant quantum computers [1]. They are expected to exhibit nonAbelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, and the pinning is predicted to be exponential as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in proximitized nanowires and atomic chains, with small modesplitting potentially explained by hybridization of Majoranas. Here, we use Coulombblockade spectroscopy in an InAs nanowire segment with epitaxial aluminum, which forms a proximityinduced superconducting Coulomb island (a Majorana island) that is isolated from normalmetal leads by tunnel barriers, to measure the splitting of nearzeroenergy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometers, subgap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half micrometer of increased wire length. For devices longer than about one micrometer, transport in strong magnetic fields occurs through a zeroenergy state that is energetically isolated from a continuum, yielding uniformly spaced Coulombblockade conductance peaks, consistent with teleportation via Majorana modes. Our results help explain the trivialtotopological transition in finite systems and to quantify the scaling of topological protection with endmode separation.
S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Nature 531, 206 (2016) [pdf] DOI: 10.1038/nature17162

Charged topological entanglement entropy 
Abstract
 A charged entanglement entropy is a new measure which probes quantum entanglement between different charge sectors. We study symmetry protected topological (SPT) phases in 2+1 dimensional spacetime by using this charged entanglement entropy. SPT phases are short range entangled states without topological order and hence cannot be detected by the topological entanglement entropy. We demonstrate that the universal part of the charged entanglement entropy is nonzero for nontrivial SPT phases and therefore it is a useful measure to detect short range entangled topological phases. We also discuss that the classification of SPT phases based on the charged topological entanglement entropy is related to that of the braiding statistics of quasiparticles.
Shunji Matsuura, Xueda Wen, LingYan Hung, Shinsei Ryu Journal reference: Phys. Rev. B 93, 195113 (2016) [pdf] DOI: 10.1103/PhysRevB.93.195113

Phasetunable Majorana bound states in a topological NSNS junction 
Abstract
 We theoretically study the differential conductance of a onedimensional normalsuperconductornormalsuperconductor (NSNS) junction with a phase bias applied between the two superconductors. We consider specifically a junction formed by a spinorbit coupled semiconducting nanowire with regions of the nanowire having superconducting pairing induced by a bulk $s$wave superconductor. When the nanowire is tuned into a topologically nontrivial phase by a Zeeman field, it hosts zeroenergy Majorana modes at its ends as well as at the interface between the two superconductors. The phasedependent splitting of the Majorana modes gives rise to features in the differential conductance that offer a clear distinction between the topologically trivial and nontrivial phases. We calculate the transport properties of the junction numerically and also present a simple analytical model that captures the main properties of the predicted tunneling spectroscopy.
Esben Bork Hansen, Jeroen Danon, Karsten Flensberg Journal reference: Phys. Rev. B 93, 094501 (2016) [pdf] DOI: 10.1103/PhysRevB.93.094501

Statistical theory of relaxation of highenergy electrons in quantum Hall edge states 
Abstract
 We investigate theoretically the energy exchange between electrons of two copropagating, outofequilibrium edge states with opposite spin polarization in the integer quantum Hall regime. A quantum dot tunnelcoupled to one of the edge states locally injects electrons at high energy. Thereby a narrow peak in the energy distribution is created at high energy above the Fermi level. A second downstream quantum dot performs an energy resolved measurement of the electronic distribution function. By varying the distance between the two dots, we are able to follow every step of the energy exchange and relaxation between the edge states  even analytically under certain conditions. In the absence of translational invariance along the edge, e.g. due to the presence of disorder, energy can be exchanged by nonmomentum conserving twoparticle collisions. For weakly broken translational invariance, we show that the relaxation is described by coupled FokkerPlanck equations. From these we find that relaxation of the injected electrons can be understood statistically as a generalized driftdiffusion process in energy space for which we determine the driftvelocity and the dynamical diffusion parameter. Finally, we provide a physically appealing picture in terms of individual edge state heating as a result of the relaxation of the injected electrons.
Anders Mathias Lunde, Simon E. Nigg Journal reference: Phys. Rev. B 94, 045409 (2016) [pdf] DOI: 10.1103/PhysRevB.94.045409

Effects of spinorbit coupling and spatial symmetries on the Josephson current in SNS junctions 
Abstract
 We present an analysis of the symmetries of the interference pattern of critical currents through a twodimensional superconductorsemiconductorsuperconductor junction, taking into account Rashba and Dresselhaus spinorbit interaction, an arbitrarily oriented magnetic field, disorder, and structural asymmetries. We relate the symmetries of the pattern to the absence or presence of symmetries in the Hamiltonian, which provides a qualitative connection between easily measurable quantities and the spinorbit coupling and other symmetries of the junction. We support our analysis with numerical calculations of the Josephson current based on a perturbative expansion up to eighth order in tunnel coupling between the normal region and the superconductors.
Asbjørn Rasmussen, Jeroen Danon, Henri Suominen, Fabrizio Nichele, Morten Kjaergaard, Karsten Flensberg Journal reference: Phys. Rev. B 93, 155406 (2016) [pdf] DOI: 10.1103/PhysRevB.93.155406

Noise Suppression Using Symmetric Exchange Gates in Spin Qubits 
Abstract
 We demonstrate a substantial improvement in the spinexchange gate using symmetric control instead of conventional detuning in GaAs spin qubits, up to a factorofsix increase in the quality factor of the gate. For symmetric operation, nanosecond voltage pulses are applied to the barrier that controls the interdot potential between quantum dots, modulating the exchange interaction while maintaining symmetry between the dots. Excellent agreement is found with a model that separately includes electrical and nuclear noise sources for both detuning and symmetric gating schemes. Unlike exchange control via detuning, the decoherence of symmetric exchange rotations is dominated by rotationaxis fluctuations due to nuclear field noise rather than direct exchange noise.
Frederico Martins, Filip K. Malinowski, Peter D. Nissen, Edwin Barnes, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. Lett. 116, 116801 (2016) [pdf] DOI: 10.1103/PhysRevLett.116.116801

Quantum impurities: from mobile Josephson junctions to depletons 
Abstract
 We overview the main features of mobile impurities moving in onedimensional superfluid backgrounds by modeling it as a mobile Josephson junction, which leads naturally to the periodic dispersion of the impurity. The dissipation processes, such as radiative friction and quantum viscosity, are shown to result from the interaction of the collective phase difference with the background phonons. We develop a more realistic depleton model of an impurityhole bound state that provides a number of exact results interpolating between the semiclassical weaklyinteracting picture and the strongly interacting TonksGirardeau regime. We also discuss the physics of a trapped impurity, relevant to current experiments with ultra cold atoms.
Michael Schecter, Dimitri M. Gangardt, Alex Kamenev Journal reference: New J. Phys. 18 (2016) 065002 [pdf] DOI: 10.1088/13672630/18/6/065002

Gatemon Benchmarking and TwoQubit Operations 
Abstract
 Recent experiments have demonstrated superconducting transmon qubits with semiconductor nanowire Josephson junctions. These hybrid gatemon qubits utilize field effect tunability characteristic for semiconductors to allow complete qubit control using gate voltages, potentially a technological advantage over conventional fluxcontrolled transmons. Here, we present experiments with a twoqubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate singlequbit gate errors below 0.7% for all gates, including voltagecontrolled $Z$ rotations. We show coherent capacitive coupling between two gatemons and coherent swap operations. Finally, we perform a twoqubit controlledphase gate with an estimated fidelity of 91%, demonstrating the potential of gatemon qubits for building scalable quantum processors.
L. Casparis, T. W. Larsen, M. S. Olsen, F. Kuemmeth, P. Krogstrup, J. Nygård, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. Lett. 116, 150505 (2016) [pdf] DOI: 10.1103/PhysRevLett.116.150505

Twodimensional epitaxial superconductorsemiconductor heterostructures: A platform for topological superconducting networks 
Abstract
 Progress in the emergent field of topological superconductivity relies on synthesis of new material combinations, combining superconductivity, low density, and spinorbit coupling (SOC). For example, theory [14] indicates that the interface between a onedimensional (1D) semiconductor (Sm) with strong SOC and a superconductor (S) hosts Majorana modes with nontrivial topological properties [58]. Recently, epitaxial growth of Al on InAs nanowires was shown to yield a high quality SSm system with uniformly transparent interfaces [9] and a hard induced gap, indicted by strongly suppressed sub gap tunneling conductance [10]. Here we report the realization of a twodimensional (2D) InAs/InGaAs heterostructure with epitaxial Al, yielding a planar SSm system with structural and transport characteristics as good as the epitaxial wires. The realization of 2D epitaxial SSm systems represent a significant advance over wires, allowing extended networks via topdown processing. Among numerous potential applications, this new material system can serve as a platform for complex networks of topological superconductors with gatecontrolled Majorana zero modes [14]. We demonstrate gateable Josephson junctions and a highly transparent 2D SSm interface based on the product of excess current and normal state resistance.
J. Shabani, M. Kjaergaard, H. J. Suominen, Younghyun Kim, F. Nichele, K. Pakrouski, T. Stankevic, R. M. Lutchyn, P. Krogstrup, R. Feidenhans'l, S. Kraemer, C. Nayak, M. Troyer, C. M. Marcus, C. J. Palmstrøm Journal reference: Phys. Rev. B 93, 155402 (2016) [pdf] DOI: 10.1103/PhysRevB.93.155402

Braiding properties of Majorana Kramers pairs 
Abstract
 We consider the braiding of Kramers pairs of Majorana bound states. We derive the most general transformation on the manybody ground state that is applied as the result of such a braiding process. The result is derived in the context of a simple toy model, but we will show that it has the most general form that is compatible with local and global conservation of electron parity. In accordance with earlier work the resulting transformation turns out to be path dependent, which shows that Kramers pairs of Majorana bound states cannot be used for topological quantum computation. We also discuss under which conditions the result is path independent and corresponds to two independent exchanges of pairs of Majorana bound states.
Konrad Wölms, Ady Stern, Karsten Flensberg Journal reference: Phys. Rev. B 93, 045417 (2016) [pdf] DOI: 10.1103/PhysRevB.93.045417

Majorana bound state in a coupled quantumdot hybridnanowire system 
Abstract
 2015

YuShibaRusinov states in phasebiased superconductor–quantum dot–superconductor junctions 
Abstract
 We study the effects of a phase difference on YuShibaRusinov (YSR) states in a spinful Coulombblockaded quantum dot contacted by a superconducting loop. In the limit where charging energy is larger than the superconducting gap, we determine the subgap excitation spectrum, the corresponding supercurrent, and the differential conductance as measured by a normalmetal tunnel probe. In absence of a phase difference only one linear combination of the superconductor lead electrons couples to the spin, which gives a single YSR state. With finite phase difference, however, it is effectively a twochannel scattering problem and therefore an additional state emerges from the gap edge. The energy of the phasedependent YSR states depend on the gate voltage and one state can cross zero energy twice inside the valley with odd occupancy. These crossings are shifted by the phase difference towards the charge degeneracy points, corresponding to larger exchange couplings. Moreover, the zeroenergy crossings give rise to resonant peaks in the differential conductance with magnitude $4e^2/h$. Finally, we demonstrate that the quantum fluctuations of the dot spin do not alter qualitatively any of the results.
Gediminas Kiršanskas, Moshe Goldstein, Karsten Flensberg, Leonid I. Glazman, Jens Paaske Journal reference: Phys. Rev. B 92, 235422 (2015) [pdf] DOI: 10.1103/PhysRevB.92.235422

Raman spectroscopy and electrical properties of InAs nanowires with local oxidation enabled by substrate microtrenches and laser irradiation 
Abstract
 The thermal gradient along indiumarsenide nanowires was engineered by a combination of fabricated micro trenches in the supporting substrate and focused laser irradiation. This allowed local control of thermally activated oxidation reactions of the nanowire on the scale of the diffraction limit. The locality of the oxidation was detected by microRaman mapping, and the results were found consistent with numerical simulations of the temperature profile. Applying the technique to nanowires in electrical devices the locally oxidized nanowires remained conducting with a lower conductance as expected for an effectively thinner conducting core.
R. Tanta, M. H. Madsen, Z. Liao, P. Krogstrup, T. Vosch, J. Nygard, T. S. Jespersen Journal reference: Appl. Phys. Lett. 107, 243101 (2015) [pdf] DOI: 10.1063/1.4937442

Patterning of high mobility electron gases at complex oxide interfaces 
Abstract
 Oxide interfaces provide an opportunity for electronics. However, patterning of electron gases at complex oxide interfaces is challenging. In particular, patterning of complex oxides while preserving a high electron mobility remains underexplored and inhibits the study of quantum mechanical effects where extended electron mean free paths are paramount. This letter presents an effective patterning strategy of both the amorphousLaAlO$_3$/SrTiO$_3$ (aLAO/STO) and modulationdoped amorphous LaAlO$_3$/La$_{7/8}$Sr$_{1/8}$MnO$_3$/SrTiO$_3$ (aLAO/LSM/STO) oxide interfaces. Our patterning is based on selective wet etching of amorphousLSM (aLSM) thin films which acts as a hard mask during subsequent depositions. Strikingly, the patterned modulationdoped interface shows electron mobilities up to ~8,700 cm$^2$/Vs at 2 K, which is among the highest reported values for patterned conducting complex oxide interfaces that usually are ~1,000 cm$^2$/Vs at 2 K.
Felix Trier, Guenevere E. D. K. Prawiroatmodjo, Merlin von Soosten, Dennis Valbjørn Christensen, Thomas Sand Jespersen, Yunzhong Chen, Nini Pryds Journal reference: Applied Physics Letters 107, 191604 (2015) [pdf] DOI: 10.1063/1.4935553

Environmental Coulomb blockade of topological superconductornormal metal junctions 
Abstract
 We study charge transport of a topological superconductor connected to different electromagnetic environments using a lowenergy description where only the Majorana bound states in the superconductor are included. Extending earlier findings who found a crossover between perfect Andreev reflection with conductance $2e^2/h$ to a regime with blocked transport when the resistance of the environment is larger than $2e^2/h$, we consider Majorana bound states coupled to metallic dots. in particular, we study two topological superconducting leads connected by a metallic quantum dot in both the weak tunneling and strong tunneling regimes. For weak tunneling, we project onto the most relevant charge states. For strong tunneling, we start from the Andreev fixed point and integrate out charge fluctuations which gives an effective lowenergy model for the nonperturbative gatevoltage modulated cotunneling current. In both regimes and in contrast to cotunneling with normal leads, the conductance is temperature independent because of the resonant Andreev reflections, which are included to all orders.
Konrad Wölms, Karsten Flensberg Journal reference: Phys. Rev. B 92, 165428 (2015) [pdf] DOI: 10.1103/PhysRevB.92.165428

Probing transverse magnetic anisotropy by electronic transport through a singlemolecule magnet 
Abstract
 By means of electronic transport, we study the transverse magnetic anisotropy of an individual Fe$_4$ singlemolecule magnet (SMM) embedded in a threeterminal junction. In particular, we determine in situ the transverse anisotropy of the molecule from the pronounced intensity modulations of the linear conductance, which are observed as a function of applied magnetic field. The proposed technique works at temperatures exceeding the energy scale of the tunnel splittings of the SMM. We deduce that the transverse anisotropy for a single Fe$_4$ molecule captured in a junction is substantially larger than the bulk value.
M. Misiorny, E. Burzurí, R. Gaudenzi, K. Park, M. Leijnse, M. R. Wegewijs, J. Paaske, A. Cornia, H. S. J. van der Zant Journal reference: Physical Review B 91, 035442 (2015) [pdf] DOI: 10.1103/PhysRevB.91.035442

Nonlocal damping of helimagnets in onedimensional interacting electron systems 
Abstract
 We investigate the magnetization relaxation of a onedimensional helimagnetic system coupled to interacting itinerant electrons. The relaxation is assumed to result from the emission of plasmons, the elementary excitations of the onedimensional interacting electron system, caused by slow changes of the magnetization profile. This dissipation mechanism leads to a highly nonlocal form of magnetization damping that is strongly dependent on the electronelectron interaction. Forward scattering processes lead to a spatially constant damping kernel, while backscattering processes produce a spatially oscillating contribution. Due to the nonlocal damping, the thermal fluctuations become spatially correlated over the entire system. We estimate the characteristic magnetization relaxation times for magnetic quantum wires and nuclear helimagnets.
Kjetil M. D. Hals, Karsten Flensberg, Mark S. Rudner Journal reference: Phys. Rev. B 92, 094403 (2015) [pdf] DOI: 10.1103/PhysRevB.92.094403

Semiclassical theory of persistent current fluctuations in ballistic chaotic rings 
Abstract
 The persistent current in a mesoscopic ring has a Gaussian distribution with small nonGaussian corrections. Here we report a semiclassical calculation of the leading nonGaussian correction, which is described by the threepoint correlation function. The semiclassical approach is applicable to systems in which the electron dynamics is ballistic and chaotic, and includes the dependence on the Ehrenfest time. At small but finite Ehrenfest times, the nonGaussian fluctuations are enhanced with respect to the limit of zero Ehrenfest time.
Piet W. Brouwer, Jeroen Danon [pdf] DOI: 10.1016/j.physe.2015.08.004 1507.05422v1 [pdf]

Spinorbit torques for current parallel and perpendicular to a domain wall 
Abstract
 We report field and currentinduced domain wall (DW) depinning experiments in Ta/Co20Fe60B20/MgO nanowires through a Hall cross geometry. While purely fieldinduced depinning shows no angular dependence on inplane fields, the effect of the current depends crucially on the internal DW structure, which we manipulate by an external magnetic inplane field. We show for the first time depinning measurements for a current sent parallel to the DW and compare its depinning efficiency with the conventional case of current flowing perpendicularly to the DW. We find that the maximum efficiency is similar for both current directions within the error bars, which is in line with a dominating dampinglike spinorbit torque (SOT) and indicates that no large additional torques arise for currents parallel to the DW. Finally, we find a varying dependence of the maximum depinning efficiency angle for different DWs and pinning levels. This emphasizes the importance of our full angular scans compared to previously used measurements for just two field directions (parallel and perpendicular to the DW) and shows the sensitivity of the spinorbit torque to the precise DW structure and pinning sites.
Tomek Schulz, Oscar Alejos, Eduardo Martinez, Kjetil M. D. Hals, Karin Garcia, Kyujoon Lee, Roberto Lo Conte, Gurucharan V. Karnad, Simone Moretti, Berthold Ocker, Dafiné Ravelosona, Arne Brataas, Mathias Kläui [pdf] DOI: 10.1063/1.4931429 1507.02435v1 [pdf]

Quantum transport in carbon nanotubes 
Abstract
 Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries, enabled by sophisticated fabrication, have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and from valley freedom. We focus on the interplay between the two. In single quantum dots defined in short lengths of nanotube, the energy levels associated with each degree of freedom, and the spinorbit coupling between them, are revealed by Coulomb blockade spectroscopy. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits, and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electronelectron interactions in one dimension strongly modifies their transport behaviour. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the wellunderstood overall picture, we also state clearly open questions for the field. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a very low level.
E. A. Laird, F. Kuemmeth, G. Steele, K. GroveRasmussen, J. Nygård, K. Flensberg, L. P. Kouwenhoven Journal reference: Rev. Mod. Phys. 87, 703 (2015) [pdf] DOI: 10.1103/RevModPhys.87.703

Spinmotive forces and currentinduced torques in ferromagnets 
Abstract
 In metallic ferromagnets, the spintransfer torque and spinmotive force are known to exhibit a reciprocal relationship. Recent experiments on ferromagnets with strong spinorbit coupling have revealed a rich complexity in the interaction between itinerant charge carriers and magnetization, but a full understanding of this coupled dynamics is lacking. Here, we develop a general phenomenology of the two reciprocal processes of charge pumping by spinmotive forces and currentdriven magnetization dynamics. The formalism is valid for spinorbit coupling of any strength and presents a systematic scheme for deriving all possible torque and chargepumping terms that obey the symmetry requirements imposed by the point group of the system. We demonstrate how the different charge pumping and torque contributions are connected via the Onsager reciprocal relations. The formalism is applied to two important classes of systems: isotropic ferromagnets with nonuniform magnetization and homogeneous ferromagnets described by the point group $C_{2v}$.
Kjetil M. D. Hals, Arne Brataas Journal reference: Phys. Rev. B 91, 214401 (2015) [pdf] DOI: 10.1103/PhysRevB.91.214401

Interaction effects on proximityinduced superconductivity in semiconducting nanowires 
Abstract
 We investigate the effect of electronelectron interactions on proximityinduced $s$wave superconductivity in onedimensional nanowires. We treat the interactions on a selfconsistent meanfield level, and find an analytic expression for the effective pairing potential in the presence of interactions, valid for a weakly tunnel coupled wire. We show that for a set of two nanowires placed in parallel on a superconducting substrate, the interactioninduced reduction of the pairing energy could result in the effective interwire pairing potential exceeding the intrawire potential, which is one of the requirements for creating a timereversal symmetric topological superconducting state in such a twowire system.
Jeroen Danon, Karsten Flensberg Journal reference: Phys. Rev. B 91, 165425 (2015) [pdf] DOI: 10.1103/PhysRevB.91.165425

SemiconductorNanowireBased Superconducting Qubit 
Abstract
 We introduce a hybrid qubit based on a semiconductor nanowire with an epitaxially grown superconductor layer. Josephson energy of the transmonlike device ("gatemon") is controlled by an electrostatic gate that depletes carriers in a semiconducting weak link region. Strong coupling to an onchip microwave cavity and coherent qubit control via gate voltage pulses is demonstrated, yielding reasonably long relaxation times (0.8 {\mu}s) and dephasing times (1 {\mu}s), exceeding gate operation times by two orders of magnitude, in these firstgeneration devices. Because qubit control relies on voltages rather than fluxes, dissipation in resistive control lines is reduced, screening reduces crosstalk, and the absence of flux control allows operation in a magnetic field, relevant for topological quantum information.
T. W. Larsen, K. D. Petersson, F. Kuemmeth, T. S. Jespersen, P. Krogstrup, J. Nygard, C. M. Marcus Journal reference: Phys. Rev. Lett. 115, 127001 (2015) [pdf] DOI: 10.1103/PhysRevLett.115.127001

SpinLattice Order in OneDimensional Conductors: Beyond the RKKY Effect 
Abstract
 We investigate magnetic order in a lattice of classical spins coupled to an isotropic gas of onedimensional (1d) conduction electrons via local exchange interactions. The frequently discussed RudermanKittelKasuyaYosida (RKKY) effective exchange model for this system predicts that spiral order is always preferred. Here we consider the problem nonperturbatively, and find that such order vanishes above a critical value of the exchange coupling that depends strongly on the lattice spacing. The critical coupling tends to zero as the lattice spacing becomes commensurate with the Fermi wave vector, signalling the breakdown of the perturbative RKKY picture, and spiral order, even at weak coupling. We provide the exact phase diagram for arbitrary exchange coupling and lattice spacing, and discuss its stability. Our results shed new light on the problem of utilizing a spiral spinlattice state to drive a onedimensional superconductor into a topological phase.
Michael Schecter, Mark S. Rudner, Karsten Flensberg Journal reference: Phys. Rev. Lett. 114, 247205 (2015) [pdf] DOI: 10.1103/PhysRevLett.114.247205

Hard gap in epitaxial semiconductor–superconductor nanowires 
Abstract
 Many present and future applications of superconductivity would benefit from electrostatic control of carrier density and tunneling rates, the hallmark of semiconductor devices. One particularly exciting application is the realization of topological superconductivity as a basis for quantum information processing. Proposals in this direction based on proximity effect in semiconductor nanowires are appealing because the key ingredients are currently in hand. However, previous instances of proximitized semiconductors show significant tunneling conductance below the superconducting gap, suggesting a continuum of subgap statesa situation that nullifies topological protection. Here, we report a hard superconducting gap induced by proximity effect in a semiconductor, using epitaxial AlInAs superconductorsemiconductor nanowires. The hard gap, along with favorable material properties and gatetunability, makes this new hybrid system attractive for a number of applications, as well as fundamental studies of mesoscopic superconductivity.
W. Chang, S. M. Albrecht, T. S. Jespersen, F. Kuemmeth, P. Krogstrup, J. Nygård, C. M. Marcus Journal reference: Nature Nanotechnology 10, 232 (2015) [pdf] DOI: 10.1038/nnano.2014.306

Parity lifetime of bound states in a proximitized semiconductor nanowire 
Abstract
 Quasiparticle excitations can compromise the performance of superconducting devices, causing high frequency dissipation, decoherence in Josephson qubits, and braiding errors in proposed Majoranabased topological quantum computers. Quasiparticle dynamics have been studied in detail in metallic superconductors but remain relatively unexplored in semiconductorsuperconductor structures, which are now being intensely pursued in the context of topological superconductivity. To this end, we introduce a new physical system comprised of a gateconfined semiconductor nanowire with an epitaxially grown superconductor layer, yielding an isolated, proximitized nanowire segment. We identify Andreevlike bound states in the semiconductor via bias spectroscopy, determine the characteristic temperatures and magnetic fields for quasiparticle excitations, and extract a parity lifetime (poisoning time) of the bound state in the semiconductor exceeding 10 ms.
A. P. Higginbotham, S. M. Albrecht, G. Kirsanskas, W. Chang, F. Kuemmeth, P. Krogstrup, T. S. Jespersen, J. Nygard, K. Flensberg, C. M. Marcus Journal reference: Nature Physics 11, 1017 (2015) [pdf] DOI: 10.1038/nphys3461

Epitaxy of semiconductor–superconductor nanowires 
Abstract
 Controlling the properties of semiconductor/metal interfaces is a powerful method for designing functionality and improving the performance of electrical devices. Recently semiconductor/superconductor hybrids have appeared as an important example where the atomic scale uniformity of the interface plays a key role for the quality of the induced superconducting gap. Here we present epitaxial growth of semiconductormetal coreshell nanowires by molecular beam epitaxy, a method that provides a conceptually new route to controlled electrical contacting of nanostructures and for designing devices for specialized applications such as topological and gatecontrolled superconducting electronics. Our materials of choice, InAs/Al, are grown with epitaxially matched single plane interfaces, and alternative semiconductor/metal combinations allowing epitaxial interface matching in nanowires are discussed. We formulate the grain growth kinetics of the metal phase in general terms of continuum parameters and bicrystal symmetries. The method realizes the ultimate limit of uniform interfaces and appears to solve the softgap problem in superconducting hybrid structures.
P. Krogstrup, N. L. B. Ziino, W. Chang, S. M. Albrecht, M. H. Madsen, E. Johnson, J. Nygård, C. M. Marcus, T. S. Jespersen Journal reference: Nature Materials 14, 400 (2015) [pdf] DOI: 10.1038/nmat4176

YuShibaRusinov states in phasebiased superconductor–quantum dot–superconductor junctions 
Abstract
 2014

Local Adiabatic Mixing of Kramers Pairs of Majorana Bound States 
Abstract
 We consider Kramers pairs of Majorana bound states under adiabatic time evolution. This is important for the prospects of using such bound states as parity qubits. We show that local adiabatic perturbations can cause a rotation in the space spanned by the Kramers pair. Hence the quantum information is unprotected against local perturbations, in contrast to the case of single localized Majorana bound states in systems with broken time reversal symmetry. We give an analytical and a numerical example for such a rotation, and specify sufficient conditions under which a rotation is avoided. We give a general scheme for determining when these conditions are satisfied, and exemplify it with a general model of a quasi 1D time reversal symmetric topological superconductor.
Konrad Wölms, Ady Stern, Karsten Flensberg Journal reference: Phys. Rev. Lett. 113, 246401 (2014) [pdf] DOI: 10.1103/PhysRevLett.113.246401

Tunnel spectroscopy of Majorana bound states in topological superconductor/quantum dot Josephson junctions 
Abstract
 We theoretically investigate electronic transport through a junction where a quantum dot (QD) is tunnel coupled on both sides to semiconductor nanowires with strong spinorbit interaction and proximityinduced superconductivity. The results are presented as stability diagrams, i.e., the differential conductance as a function of the bias voltage applied across the junction and the gate voltage used to control the electrostatic potential on the QD. A small applied magnetic field splits and modifies the resonances due to the Zeeman splitting of the QD level. Above a critical field strength, Majorana bound states (MBS) appear at the interfaces between the two superconducting nanowires and the QD, resulting in a qualitative change of the entire stability diagram, suggesting this setup as a promising platform to identify MBS. Our calculations are based on a nonequilibrium Green's function description and is exact when Coulomb interactions on the QD can be neglected. In addition, we develop a simple pictorial view of the involved transport processes, which is equivalent to a description in terms of multiple Andreev reflections, but provides an alternative way to understand the role of the QD level in enhancing transport for certain gate and bias voltages. We believe that this description will be useful in future studies of interacting QDs coupled to superconducting leads (with or without MBS), where it can be used to develop a perturbation expansion in the tunnel coupling.
GuangYao Huang, Martin Leijnse, Karsten Flensberg, Hongqi Xu Journal reference: Phys. Rev. B 90, 214507 (2014) [pdf] DOI: 10.1103/PhysRevB.90.214507

Gilbert Damping in Noncollinear Ferromagnets 
Abstract
 The precession and damping of a collinear magnetization displaced from its equilibrium are described by the LandauLifshitzGilbert equation. For a noncollinear magnetization, it is not known how the damping should be described. We use firstprinciples scattering theory to investigate the damping in onedimensional transverse domain walls (DWs) of the important ferromagnetic alloy Ni$_{80}$Fe$_{20}$ and interpret the results in terms of phenomenological models. The damping is found to depend not only on the magnetization texture but also on the specific dynamic modes of Bloch and N\'eel DWs. Even in the highly disordered Ni$_{80}$Fe$_{20}$ alloy, the damping is found to be remarkably nonlocal.
Zhe Yuan, Kjetil M. D. Hals, Yi Liu, Anton A. Starikov, Arne Brataas, Paul J. Kelly Journal reference: Physical Review Letters 113, 266603 (2014) [pdf] DOI: 10.1103/PhysRevLett.113.266603

Magnonic charge pumping via spin–orbit coupling 
Abstract
 The interplay between spin, charge, and orbital degrees of freedom has led to the development of spintronic devices like spintorque oscillators, spinlogic devices, and spintransfer torque magnetic randomaccess memories. In this development spin pumping, the process where pure spincurrents are generated from magnetisation precession, has proved to be a powerful method for probing spin physics and magnetisation dynamics. The effect originates from direct conversion of low energy quantised spinwaves in the magnet, known as magnons, into a flow of spins from the precessing magnet to adjacent normal metal leads. The spinpumping phenomenon represents a convenient way to electrically detect magnetisation dynamics, however, precessing magnets have been limited so far to pump pure spin currents, which require a secondary spincharge conversion element such as heavy metals with large spin Hall angle or multilayer layouts to be detectable. Here, we report the experimental observation of charge pumping in which a precessing ferromagnet pumps a charge current, demonstrating direct conversion of magnons into highfrequency currents via the relativistic spinorbit interaction. The generated electric current, differently from spin currents generated by spinpumping, can be directly detected without the need of any additional spin to charge conversion mechanism and amplitude and phase information about the relativistic currentdriven magnetisation dynamics. The chargepumping phenomenon is generic and gives a deeper understanding of the recently observed spinorbit torques, of which it is the reciprocal effect and which currently attract interest for their potential in manipulating magnetic information. Furthermore, charge pumping provides a novel link between magnetism and electricity and may find application in sourcing alternating electric currents.
Chiara Ciccarelli, Kjetil M. D. Hals, Andrew Irvine, Vit Novak, Yaroslav Tserkovnyak, Hidekazu Kurebayashi, Arne Brataas, Andrew Ferguson [pdf] DOI: 10.1038/nnano.2014.252 1411.2779v1 [pdf]

Designing

Abstract
 We propose and analyze a new way of using $\pi$ stacking to design molecular junctions that either enhance or suppress a phononic heat current, but at the same time remain conductors for an electric current. Such functionality is highly desirable in thermoelectric energy converters, as well as in other electronic components where heat dissipation should be minimized or maximized. We suggest a molecular design consisting of two masses coupled to each other with one mass coupled to each lead. By having a small coupling (spring constant) between the masses, it is possible to either reduce, or perhaps more surprisingly enhance the phonon conductance. We investigate a simple model system to identify optimal parameter regimes and then use first principle calculations to extract model parameters for a number of specific molecular realizations, confirming that our proposal can indeed be realized using standard molecular building blocks.
Gediminas Kiršanskas, Qian Li, Karsten Flensberg, Gemma C. Solomon, Martin Leijnse Journal reference: Appl. Phys. Lett. 105, 233102 (2014) [pdf] DOI: 10.1063/1.4903340

Quantum interference in offresonant transport through single molecules 
Abstract
 We provide a simple set of rules for predicting interference effects in offresonant transport through singlemolecule junctions. These effects fall in two classes, showing respectively an odd or an even number of nodes in the linear conductance within a given molecular charge state, and we demonstrate how to decide the interference class directly from the contacting geometry. For neutral alternant hydrocarbons, we employ the CoulsonRushbrookeMcLachlan pairing theorem to show that the interference class is decided simply by tunneling on and off the molecule from same, or different sublattices. More generally, we investigate a range of smaller molecules by means of exact diag onalization combined with a perturbative treatment of the moleculelead tunnel coupling. While these results generally agree well with GW calculations, they are shown to be at odds with simpler meanfield treatments. For molecules with spindegenerate ground states, we show that for most junctions, interference causes no transmission nodes, but argue that it may lead to a nonstandard gatedependence of the zerobias Kondo resonance.
Kim G. L. Pedersen, Mikkel Strange, Martin Leijnse, Per Hedegård, Gemma Solomon, Jens Paaske Journal reference: Phys. Rev. B 90, 125413 (2014) [pdf] DOI: 10.1103/PhysRevB.90.125413

Multilevel Interference Resonances in Strongly Driven ThreeLevel Systems 
Abstract
 We study multiphoton resonances in a stronglydriven threelevel quantum system, where one level is periodically swept through a pair of levels with constant energy separation $E$. Near the multiphoton resonance condition $n\hbar\omega = E$, where $n$ is an integer, we find qualitatively different behavior for $n$ even or odd. We explain this phenomenon in terms of families of interfering trajectories of the multilevel system. Remarkably, the behavior is insensitive to fluctuations of the energy of the driven level, and survives deep into the strong dephasing regime. The setup can be relevant for a variety of solid state and atomic or molecular systems. In particular, it provides a clear mechanism to explain recent puzzling experimental observations in stronglydriven double quantum dots.
Jeroen Danon, Mark S. Rudner Journal reference: Phys. Rev. Lett. 113, 247002 (2014) [pdf] DOI: 10.1103/PhysRevLett.113.247002

Hole Spin Coherence in a Ge/Si Heterostructure Nanowire 
Abstract
 Relaxation and dephasing of hole spins are measured in a gatedefined Ge/Si nanowire double quantum dot using a fast pulsedgate method and dispersive readout. An inhomogeneous dephasing time $T_2^* \sim 0.18~\mathrm{\mu s}$ exceeds corresponding measurements in IIIV semiconductors by more than an order of magnitude, as expected for predominately nuclearspinfree materials. Dephasing is observed to be exponential in time, indicating the presence of a broadband noise source, rather than Gaussian, previously seen in systems with nuclearspindominated dephasing.
A. P. Higginbotham, T. W. Larsen, J. Yao, H. Yan, C. M. Lieber, C. M. Marcus, F. Kuemmeth Journal reference: Nano Letters 14, 3582 (2014) [pdf] DOI: 10.1021/nl501242b

Spinwaveinduced correction to the conductivity of ferromagnets 
Abstract
 We calculate the correction to the conductivity of a disordered ferromagnetic metal due to spinwavemediated electronelectron interactions. This correction is the generalization of the AltshulerAronov correction to spinwavemediated interactions. We derive a general expression for the conductivity correction to lowest order in the spinwavemediated interaction and for the limit that the exchange splitting $\Delta$ is much smaller than the Fermi energy. For a "clean" ferromagnet with $\Delta\tau_{\rm el}/\hbar \gg 1$, with $\tau_{\rm el}$ the mean time for impurity scattering, we find a correction $\delta \sigma \propto T^{5/2}$ at temperatures $T$ above the spin wave gap. In the opposite, "dirty" limit, $\Delta\tau_{\rm el}/\hbar \ll 1$, the correction is a nonmonotonous function of temperature.
Jeroen Danon, Alessandro Ricottone, Piet W. Brouwer Journal reference: Phys. Rev. B 90, 024405 (2014) [pdf] DOI: 10.1103/PhysRevB.90.024405

Majorana Bound States in TwoChannel TimeReversalSymmetric Nanowire Systems 
Abstract
 We consider timereversalsymmetric twochannel semiconducting quantum wires proximity coupled to an swave superconductor. We analyze the requirements for a nontrivial topological phase and find that necessary conditions are 1) the determinant of the pairing matrix in channel space must be negative, 2) inversion symmetry must be broken, and 3) the two channels must have different spinorbit couplings. The first condition can be implemented in semiconducting nanowire systems where interactions suppress intrachannel pairing, while the inversion symmetry can be broken by tuning the chemical potentials of the channels. For the case of collinear spinorbit directions, we find a general expression for the topological invariant by block diagonalization into two blocks with chiral symmetry only. By projection to the lowenergy sector, we solve for the zero modes explicitly and study the details of the gap closing, which in the general case happens at finite momenta.
Erikas Gaidamauskas, Jens Paaske, Karsten Flensberg Journal reference: Phys. Rev. Lett. 122, 126402 (2014) [pdf] DOI: 10.1103/PhysRevLett.112.126402

Antilocalization of Coulomb Blockade in a Ge/Si Nanowire 
Abstract
 The distribution of Coulomb blockade peak heights as a function of magnetic field is investigated experimentally in a GeSi nanowire quantum dot. Strong spinorbit coupling in this holegas system leads to antilocalization of Coulomb blockade peaks, consistent with theory. In particular, the peak height distribution has its maximum away from zero at zero magnetic field, with an average that decreases with increasing field. Magnetoconductance in the openwire regime places a bound on the spinorbit length ($l_{so}$ < 20 nm), consistent with values extracted in the Coulomb blockade regime ($l_{so}$ < 25 nm).
A. P. Higginbotham, F. Kuemmeth, T. W. Larsen, M. Fitzpatrick, J. Yao, H. Yan, C. M. Lieber, C. M. Marcus Journal reference: Phys. Rev. Lett. 112, 216806 (2014) [pdf] DOI: 10.1103/PhysRevLett.112.216806

Dynamics of spinflip photonassisted tunneling 
Abstract
 We present timeresolved measurements of spinflip photonassisted tunneling and spinflip relaxation in a doubly occupied double quantum dot. The photonassisted excitation rate as a function of magnetic field indicates that spinorbit coupling is the dominant mechanism behind the spinflip under the present conditions. We are able to extract the resulting effective `spinflip tunneling' energy, which is found to be three orders of magnitude smaller than the regular spinconserving tunneling energy. We also measure the relaxation and dephasing times of a qubit formed out of two twoelectron states with different spin and charge configurations.
F. R. Braakman, J. Danon, L. R. Schreiber, W. Wegscheider, L. M. K. Vandersypen Journal reference: Phys. Rev. B 89, 075417 (2014) [pdf] DOI: 10.1103/PhysRevB.89.075417

Coherent Operations and Screening in Multielectron Spin Qubits 
Abstract
 The performance of multielectron spin qubits is examined by comparing exchange oscillations in coupled singleelectron and multielectron quantum dots in the same device. Fast (> 1 GHz) exchange oscillations with a quality factor Q > 15 are found for the multielectron case, compared to Q ~ 2 for the singleelectron case, the latter consistent with previous experiments. A model of dephasing that includes voltage and hyperfine noise is developed that is in good agreement with both single and multielectron data, though in both cases additional exchangeindependent dephasing is needed to obtain quantitative agreement across a broad parameter range.
A. P. Higginbotham, F. Kuemmeth, M. P. Hanson, A. C. Gossard, C. M. Marcus Journal reference: Phys. Rev. Lett. 112, 026801 (2014) [pdf] DOI: 10.1103/PhysRevLett.112.026801

Local Adiabatic Mixing of Kramers Pairs of Majorana Bound States 
Abstract
 2013

Spinwaveinduced corrections to the electronic density of states in metallic ferromagnets 
Abstract
 We calculate the correction to the electronic density of states in a disordered ferromagnetic metal induced by spinwave mediated interaction between the electrons. Our calculation is valid for the case that the exchange splitting in the ferromagnet is much smaller than the Fermi energy, but we make no assumption on the relative magnitude of the exchange splitting and the elastic electronic scattering time. In the "clean limit", where the exchange splitting is much larger than the electronic scattering rate, we find a correction with a T^{d/2} temperature dependence, where d is the effective dimensionality of the ferromagnet. In the opposite "dirty limit" the densityofstates correction is a nonmonotonous function of energy and temperature.
Alessandro Ricottone, Jeroen Danon, Piet W. Brouwer [pdf] DOI: 10.1088/13672630/15/12/123036 1310.3511v1 [pdf]

Epitaxial aluminum contacts to InAs nanowires 
Abstract
 We report a method for making epitaxial superconducting contacts to semiconducting nanowires. The temperature and gate characteristics demonstrate barrierfree electrical contact, and the properties in the superconducting state are investigated at low temperature. Halfcovering aluminum contacts are realized without the need of lithography and we demonstrate how to controllably insert highband gap layers in the interface region. These developments are relevant to hybrid superconductornanowire devices that support Majorana zero energy states.
 1309.4569v1 [pdf]
N. L. B. Ziino, P. Krogstrup, M. H. Madsen, E. Johnson, J. B. Wagner, C. M. Marcus, J. Nygård, T. S. Jespersen [pdf]

Theory of coherent dynamic nuclear polarization in quantum dots 
Abstract
 We consider the dynamic nuclear spin polarization (DNP) using two electrons in a double quantum dot in presence of external magnetic field and spinorbit interaction, in various schemes of periodically repeated sweeps through the ST+ avoided crossing. By treating the problem semiclassically, we find that generally the DNP have two distinct contributions  a geometrical polarization and a dynamic polarization, which have different dependence on the control parameters such as the sweep rates and waiting times in each period. Both terms show nontrivial dependence on those control parameter. We find that even for small spinorbit term, the dynamical polarization dominates the DNP in presence of a long waiting period near the ST+ avoided crossing, of the order of the nuclear Larmor precession periods. A detailed numerical analysis of a specific control regime can explain the oscillations observed by Foletti et.~al.~in arXiv:0801.3613.
Izhar Neder, Mark S. Rudner, Bertrand I. Halperin [pdf] DOI: 10.1103/PhysRevB.89.085403 1309.3027v1 [pdf]

Hyperfine interactions in twodimensional HgTe topological insulators 
Abstract
 We study the hyperfine interaction between the nuclear spins and the electrons in a HgTe quantum well, which is the prime experimentally realized example of a twodimensional topological insulator. The hyperfine interaction is a naturally present, internal source of broken timereversal symmetry from the point of view of the electrons. The HgTe quantum well is described by the socalled BernevigHughesZhang (BHZ) model. The basis states of the BHZ model are combinations of both S and Plike symmetry states, which means that three kinds of hyperfine interactions play a role: (i) The Fermi contact interaction, (ii) the dipoledipole like coupling and (iii) the electron orbital to nuclearspin coupling. We provide benchmark results for the forms and magnitudes of these hyperfine interactions within the BHZ model, which give a good starting point for evaluating hyperfine interactions in any HgTe nanostructure. We apply our results to the helical edge states of a HgTe twodimensional topological insulator and show how their total hyperfine interaction becomes anisotropic and dependent on the orientation of the sample edge within the plane. Moreover, for the helical edge states the hyperfine interactions due to the Plike states can dominate over the Slike contribution in certain circumstances.
Anders Mathias Lunde, Gloria Platero Journal reference: Phys. Rev. B 88, 115411 (2013) [pdf] DOI: 10.1103/PhysRevB.88.115411

Coupling Spin Qubits via Superconductors 
Abstract
 We show how superconductors can be used to couple, initialize, and read out spatially separated spin qubits. When two singleelectron quantum dots are tunnel coupled to the same superconductor, the singlet component of the twoelectron state partially leaks into the superconductor via crossed Andreev reflection. This induces a gatecontrolled singlettriplet splitting which, with an appropriate superconductor geometry, remains large for dot separations within the superconducting coherence length. Furthermore, we show that when two doubledot singlettriplet qubits are tunnel coupled to a superconductor with finite charging energy, crossed Andreev reflection enables a strong twoqubit coupling over distances much larger than the coherence length.
Martin Leijnse, Karsten Flensberg Journal reference: Phys. Rev. Lett. 111, 060501 (2013) [pdf] DOI: 10.1103/PhysRevLett.111.060501

Direct observation of interface and nanoscale compositional modulation in ternary IIIAs heterostructure nanowires 
Abstract
 Straight, axial InAs nanowire with multiple segments of GaInAs were grown. High resolution Xray energydispersive spectroscopy (EDS) mapping reveal the distribution of group III atoms at the axial interfaces and at the sidewalls. Significant Ga enrichment, accompanied by a structural change is observed at the GaInAs/InAs interfaces and a higher Ga concentration for the early grown GaInAs segments. The elemental map and EDS line profile infer Ga enrichment at the facet junctions between the sidewalls. The relative chemical potentials of ternary alloys and the thermodynamic driving force for liquid to solid transition explains the growth mechanisms behind the enrichment.
Sriram Venkatesan, Morten H. Madsen, Herbert Schmid, Peter Krogstrup, Erik Johnson, Christina Scheu Journal reference: Appl. Phys. Lett. 103, 063106 (2013) [pdf] DOI: 10.1063/1.4818338

Temperaturedependent dynamical nuclear polarization bistabilities in double quantum dots in the spinblockade regime 
Abstract
 The interplay of dynamical nuclear polarization (DNP) and leakage current through a double quantum dot in the spinblockade regime is analyzed. A finite DNP is built up due to a competition between hyperfine (HF) spinflip transitions and another inelastic escape mechanism from the triplets, which block transport. We focus on the temperature dependence of the DNP for zero energydetuning (i.e. equal electrostatic energy of one electron in each dot and a singlet in the right dot). Our main result is the existence of a transition temperature, below which the DNP is bistable, so a hysteretic leakage current versus external magnetic field B appears. This is studied in two cases: (i) Close to the crossing of the three triplet energy levels near B=0, where spinblockade is lifted due to the inhomogeneity of the effective magnetic field from the nuclei. (ii) At higher Bfields, where the two spinpolarized triplets simultaneously cross two different singlet energy levels. We develop simplified models leading to different transition temperatures T_TT and T_ST for the crossing of the triplet levels and the singlettriplet level crossings, respectively. We find T_TT analytically to be given solely by the HF couplings, whereas T_ST depends on various parameters and T_ST>T_TT. The key idea behind the existence of the transition temperatures at zero energydetuning is the suppression of energy absorption compared to emission in the inelastic HF transitions. Finally, by comparing the rate equation results with Monte Carlo simulations, we discuss the importance of having both HF interaction and another escape mechanism from the triplets to induce a finite DNP.
Anders Mathias Lunde, Carlos LópezMonís, Ioanna A. Vasiliadou, Luis L. Bonilla, Gloria Platero Journal reference: Phys. Rev. B 88, 035317 (2013) [pdf] DOI: 10.1103/PhysRevB.88.035317

Advances in the theory of III–V nanowire growth dynamics 
Abstract
 Nanowire (NW) crystal growth via the vapour_liquid_solid mechanism is a complex dynamic process involving interactions between many atoms of various thermodynamic states. With increasing speed over the last few decades many works have reported on various aspects of the growth mechanisms, both experimentally and theoretically. We will here propose a general continuum formalism for growth kinetics based on thermodynamic parameters and transition state kinetics. We use the formalism together with key elements of recent research to present a more overall treatment of III_V NW growth, which can serve as a basis to model and understand the dynamical mechanisms in terms of the basic control parameters, temperature and pressures/beam fluxes. Selfcatalysed GaAs NW growth on Si substrates by molecular beam epitaxy is used as a model system.
Peter Krogstrup, Henrik I. Jørgensen, Erik Johnson, Morten Hannibal Madsen, Claus B. Sørensen, Anna Fontcuberta i Morral, Martin Aagesen, Jesper Nygård, Frank Glas Journal reference: J. Phys. D: Appl. Phys. 46 (2013) 313001 [pdf] DOI: 10.1088/00223727/46/31/313001

In vivo magnetic resonance imaging of hyperpolarized silicon particles 
Abstract
 Siliconbased micro and nanoparticles have gained popularity in a wide range of biomedical applications due to their biocompatibility and biodegradability invivo, as well as a flexible surface chemistry, which allows drug loading, functionalization and targeting. Here we report direct invivo imaging of hyperpolarized 29Si nuclei in silicon microparticles by MRI. Natural physical properties of silicon provide surface electronic states for dynamic nuclear polarization (DNP), extremely long depolarization times, insensitivity to the invivo environment or particle tumbling, and surfaces favorable for functionalization. Potential applications to gastrointestinal, intravascular, and tumor perfusion imaging at subpicomolar concentrations are presented. These results demonstrate a new backgroundfree imaging modality applicable to a range of inexpensive, readily available, and biocompatible Si particles.
M. C. Cassidy, H. R. Chan, B. D. Ross, P. K. Bhattacharya, C. M. Marcus Journal reference: Nature Nanotechnology 8, 363 (2013) [pdf] DOI: 10.1038/nnano.2013.65

Synthesis of Long

Abstract
 We describe the synthesis, materials characterization and dynamic nuclear polarization (DNP) of amorphous and crystalline silicon nanoparticles for use as hyperpolarized magnetic resonance imaging (MRI) agents. The particles were synthesized by means of a metathesis reaction between sodium silicide (Na4Si4) and silicon tetrachloride (SiCl4) and were surface functionalized with a variety of passivating ligands. The synthesis scheme results in particles of diameter ~10 nm with long sizeadjusted 29Si spin lattice relaxation (T1) times (> 600 s), which are retained after hyperpolarization by low temperature DNP.
Tonya M. Atkins, Maja C. Cassidy, Menyoung Lee, Shreyashi Ganguly, Charles M. Marcus, Susan M. Kauzlarich Journal reference: ACS Nano 7, 1609 (2013) [pdf] DOI: 10.1021/nn305462y

QuantumDotBased Resonant Exchange Qubit 
Abstract
 We introduce a solidstate qubit in which exchange interactions among confined electrons provide both the static longitudinal field and the oscillatory transverse field, allowing rapid and full qubit control via rf gatevoltage pulses. We demonstrate twoaxis control at a detuning sweetspot, where leakage due to hyperfine coupling is suppressed by the large exchange gap. A {\pi}/2gate time of 2.5 ns and a coherence time of 19 {\mu}s, using multipulse echo, are also demonstrated. Model calculations that include effects of hyperfine noise are in excellent quantitative agreement with experiment.
J. Medford, J. Beil, J. M. Taylor, E. I. Rashba, H. Lu, A. C. Gossard, C. M. Marcus Journal reference: Phys. Rev. Lett. 111, 050501 (2013) [pdf] DOI: 10.1103/PhysRevLett.111.050501

Interaction effects in electric transport through selfassembled molecular monolayers 
Abstract
 We theoretically investigate the effect of intermolecular Coulomb interactions on transport through molecular monolayers (or other devices based on a large number of nanoscale conductors connected in parallel). Due to the interactions, the current through different molecules become correlated, resulting in distinct features in the nonlinear currentvoltage characteristics, as we show by deriving and solving a type of modified master equation, suitable for describing transport through an infinite number of interacting conductors. Furthermore, if some of the molecules fail to bond to both electrodes, charge traps can be induced at high voltages and block transport through neighboring molecules, resulting in negative differential resistance.
Martin Leijnse Journal reference: Phys. Rev. B 87, 125417 (2013) [pdf] DOI: 10.1103/PhysRevB.87.125417

Pauli Spin Blockade and the Ultrasmall Magnetic Field Effect 
Abstract
 Based on the spinblockade model for organic magnetoresistance we present an analytic expression for the polaronbipolaron transition rate, taking into account the effective nuclear fields on the sites. We reveal the physics producing qualitatively different magnetoconductance line shapes as well as the ultrasmall magnetic field effect, and we study the role of the ratio between the intersite hopping rate and the typical magnitude of the nuclear fields. Our findings are in agreement with recent experiments and numerical simulations.
Jeroen Danon, Xuhui Wang, Aurélien Manchon [pdf] DOI: 10.1103/PhysRevLett.111.066802 1303.5852v1 [pdf]

Superconductornanowire devices from tunneling to the multichannel regime: Zerobias oscillations and magnetoconductance crossover 
Abstract
 We present transport measurements in superconductornanowire devices with a gated constriction forming a quantum point contact. Zerobias features in tunneling spectroscopy appear at finite magnetic fields, and oscillate in amplitude and split away from zero bias as a function of magnetic field and gate voltage. A crossover in magnetoconductance is observed: Magnetic fields above ~ 0.5 T enhance conductance in the lowconductance (tunneling) regime but suppress conductance in the highconductance (multichannel) regime. We consider these results in the context of Majorana zero modes as well as alternatives, including Kondo effect and analogs of 0.7 structure in a disordered nanowire.
H. O. H. Churchill, V. Fatemi, K. GroveRasmussen, M. T. Deng, P. Caroff, H. Q. Xu, C. M. Marcus Journal reference: Phys. Rev. B 87, 241401(R) (2013) [pdf] DOI: 10.1103/PhysRevB.87.241401

Spinflip phononmediated charge relaxation in double quantum dots 
Abstract
 We theoretically study the $(1,1)$ triplet to $(0,2)$ singlet relaxation rate in a lateral gatedefined double quantum dot tuned to the regime of Pauli spin blockade. We present a detailed derivation of the effective phonon density of states for this specific charge transition, keeping track of the contribution from piezoelectric as well as deformation potential electronphonon coupling. We further investigate two different spinmixing mechanisms which can couple the triplet and singlet states: a magnetic field gradient over the double dot (relevant at low external magnetic field) and spinorbit interaction (relevant at high field), and we also indicate how the two processes could interfere at intermediate magnetic field. Finally, we show how to combine all results and evaluate the relaxation rate for realistic system parameters.
J. Danon [pdf] DOI: 10.1103/PhysRevB.88.075306 1302.7169v1 [pdf]

Selfconsistent measurement and state tomography of an exchangeonly spin qubit 
Abstract
 We report initialization, complete electrical control, and singleshot readout of an exchangeonly spin qubit. Full control via the exchange interaction is fast, yielding a demonstrated 75 qubit rotations in under 2 ns. Measurement and state tomography are performed using a maximumlikelihood estimator method, allowing decoherence, leakage out of the qubit state space, and measurement fidelity to be quantified. The methods developed here are generally applicable to systems with state leakage, noisy measurements, and nonorthogonal control axes.
J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, C. M. Marcus Journal reference: Nature Nanotechnology 8, 654 (2013) [pdf] DOI: 10.1038/nnano.2013.168

Observation and spectroscopy of a twoelectron Wigner molecule in an ultraclean carbon nanotube 
Abstract
 Coulomb interactions can have a decisive effect on the ground state of electronic systems. The simplest system in which interactions can play an interesting role is that of two electrons on a string. In the presence of strong interactions the two electrons are predicted to form a Wigner molecule, separating to the ends of the string due to their mutual repulsion. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet to date a direct measurement of such a spectrum in a controllable onedimensional setting is still missing. Here we use an ultraclean suspended carbon nanotube to realize this system in a tunable potential. Using tunneling spectroscopy we measure the excitation spectra of two interacting carriers, electrons or holes, and identify seven lowenergy states characterized by their spin and isospin quantum numbers. These states fall into two multiplets according to their exchange symmetries. The formation of a stronglyinteracting Wigner molecule is evident from the small energy splitting measured between the two multiplets, that is quenched by an order of magnitude compared to the noninteracting value. Our ability to tune the twoelectron state in space and to study it for both electrons and holes provides an unambiguous demonstration of the fundamental Wigner molecule state.
S. Pecker, F. Kuemmeth, A. Secchi, M. Rontani, D. C. Ralph, P. L. McEuen, S. Ilani Journal reference: Nature Physics 9, 576581 (2013) [pdf] DOI: 10.1038/nphys2692

Singlenanowire solar cells beyond the Shockley–Queisser limit 
Abstract
 Light management is of great importance to photovoltaic cells, as it determines the fraction of incident light entering the device. An optimal pnjunction combined with an optimal light absorption can lead to a solar cell efficiency above the ShockleyQueisser limit. Here, we show how this is possible by studying photocurrent generation for a single coreshell pin junction GaAs nanowire solar cell grown on a silicon substrate. At one sun illumination a short circuit current of 180 mA/cm^2 is obtained, which is more than one order of magnitude higher than what would be predicted from LambertBeer law. The enhanced light absorption is shown to be due to a light concentrating property of the standing nanowire as shown by photocurrent maps of the device. The results imply new limits for the maximum efficiency obtainable with IIIV based nanowire solar cells under one sun illumination.
Peter Krogstrup, Henrik Ingerslev Jørgensen, Martin Heiss, Olivier Demichel, Jeppe V. Holm, Martin Aagesen, Jesper Nygard, Anna Fontcuberta i Morral Journal reference: Nature Photonics 7, 306310 (2013) [pdf] DOI: 10.1038/nphoton.2013.32

Tunneling Spectroscopy of Quasiparticle Bound States in a Spinful Josephson Junction 
Abstract
 The spectrum of a segment of InAs nanowire, confined between two superconducting leads, was measured as function of gate voltage and superconducting phase difference using a third normalmetal tunnel probe. Subgap resonances for odd electron occupancyinterpreted as bound states involving a confined electron and a quasiparticle from the superconducting leads, reminiscent of YuShibaRusinov statesevolve into Kondorelated resonances at higher magnetic fields. An additional zero bias peak of unknown origin is observed to coexist with the quasiparticle bound states.
W. Chang, V. E. Manucharyan, T. S. Jespersen, J. Nygard, C. M. Marcus Journal reference: Phys. Rev. Lett. 110, 217005 (2013) [pdf] DOI: 10.1103/PhysRevLett.110.217005

Doping incorporation paths in catalystfree Bedoped GaAs nanowires 
Abstract
 The incorporation paths of Be in GaAs nanowires grown by the Gaassisted method in molecular beam epitaxy has been investigated by electrical measurements of nanowires with different doping profiles. We find that Be atoms incorporate preferentially via the nanowire side facets, while the incorporation path through the Ga droplet is negligible. We also demonstrate that Be can diffuse into the volume of the nanowire giving an alternative incorporation path. This work is an important step towards controlled doping of nanowires and will serve as a help for designing future devices based on nanowires.
Alberto Casadei, Peter Krogstrup, Martin Heiss, Jason A. Röhr, Carlo Colombo, Thibaud Ruelle, Shivendra Upadhyay, Claus B. Sørensen, Jesper Nygård, Anna Fontcuberta i Morral Journal reference: Appl. Phys. Lett. 102, 013117 (2013) [pdf] DOI: 10.1063/1.4772020

Radicalfree dynamic nuclear polarization using electronic defects in silicon 
Abstract
 Direct dynamic nuclear polarization of 1H nuclei in frozen water and waterethanol mixtures is demonstrated using silicon nanoparticles as the polarizing agent. Electron spins at danglingbond sites near the silicon surface are identified as the source of the nuclear hyperpolarization. This novel polarization method open new avenues for the fabrication of surface engineered nanostructures to create high nuclearspin polarized solutions without introducing contaminating radicals, and for the study of molecules adsorbed onto surfaces.
M. C. Cassidy, C. Ramanathan, D. G. Cory, J. W. Ager, C. M. Marcus Journal reference: Phys. Rev. B 87, 161306(R) (2013) [pdf] DOI: 10.1103/PhysRevB.87.161306

Spinwaveinduced corrections to the electronic density of states in metallic ferromagnets 
Abstract
 2012

Introduction to topological superconductivity and Majorana fermions 
Abstract
 This short review article provides a pedagogical introduction to the rapidly growing research field of Majorana fermions in topological superconductors. We first discuss in some details the simplest "toy model" in which Majoranas appear, namely a onedimensional tightbinding representation of a pwave superconductor, introduced more than ten years ago by Kitaev. We then give a general introduction to the remarkable properties of Majorana fermions in condensed matter systems, such as their intrinsically nonlocal nature and exotic exchange statistics, and explain why these quasiparticles are suspected to be especially well suited for lowdecoherence quantum information processing. We also discuss the experimentally promising (and perhaps already successfully realized) possibility of creating topological superconductors using semiconductors with strong spinorbit coupling, proximitycoupled to standard swave superconductors and exposed to a magnetic field. The goal is to provide an introduction to the subject for experimentalists or theorists who are new to the field, focusing on the aspects which are most important for understanding the basic physics. The text should be accessible for readers with a basic understanding of quantum mechanics and second quantization, and does not require knowledge of quantum field theory or topological states of matter.
Martin Leijnse, Karsten Flensberg Journal reference: Semicond. Sci. Technol. 27, 124003 (2012) [pdf] DOI: 10.1088/02681242/27/12/124003

Parity qubits and poor man's Majorana bound states in double quantum dots 
Abstract
 We study a double quantum dot connected via a common superconducting lead and show that this system can be tuned to host one Majorana bound state (MBS) on each dot. We call them "poor man's Majorana bound states" since they are not topologically protected, but otherwise share the properties of MBS formed in topological superconductors. We describe the conditions for the existence of the two spatially separated MBS, which include breaking of spin degeneracy in the two dots, with the spins polarized in different directions. Therefore, we propose to use a magnetic field configuration where the field directions on the two dot form an angle. By control of this angle the cross Andreev reflection and the tunnel amplitudes can be tuned to be approximately equal, which is a requirement for the formation of the MBS. We show that the fermionic state encoded in the two Majoranas constitutes a parity qubit, which is nonlocal and can only be measured by probing both dots simultaneously. Using a manyparticle basis for the MBS, we discuss the role of interactions and show that interdot interactions always lift the degeneracy. We also show how the MBS can be probed by transport measurements and discuss how the combination of several such double dot systems allows for entanglement of parity qubits and measurement of their dephasing times.
Martin Leijnse, Karsten Flensberg Journal reference: Phys. Rev. B. 86, 134528 (2012) [pdf] DOI: 10.1103/PhysRevB.86.134528


Abstract
 We demonstrate gate control of the electronic gtensor in single and double quantum dots formed along a bend in a carbon nanotube. From the dependence of the singledot excitation spectrum on magnetic field magnitude and direction, we extract spinorbit coupling, valley coupling, spin and orbital magnetic moments. Gate control of the gtensor is measured using the splitting of the Kondo peak in conductance as a sensitive probe of Zeeman energy. In the double quantum dot regime, the magnetic field dependence of the position of cotunneling lines in the two dimensional charge stability diagram is used to infer the positions of the two dots along the nanotube.
R. A. Lai, H. O. H. Churchill, C. M. Marcus Journal reference: Physical Review B 89, 121303(R) 2014 [pdf] DOI: 10.1103/PhysRevB.89.121303

Finitebias conductance anomalies at a singlettriplet crossing 
Abstract
 Quantum dots and singlemolecule transistors may exhibit level crossings induced by tuning external parameters such as magnetic field or gate voltage. For Coulomb blockaded devices, this shows up as an inelastic cotunneling threshold in the differential conductance, which can be tuned to zero at the crossing. Here we show that, in addition, level crossings can give rise to a nearly vertical stepedge, ridge or even a Fanolike ridgevalley feature in the differential conductance inside the relevant Coulomb diamond. We study a gatetunable quasidegeneracy between singlet and triplet ground states, and demonstrate how these different shapes may result from a competition between nonequilibrium occupations and weak (spinorbit) mixing of the states. Our results are shown to be in qualitative agreement with recent transport measurements on a Mn complex [E. A. Osorio, et al., Nano Lett. 10, 105 (2010)]. The effect remains entirely general and should be observable in a wide range of Coulomb blockaded devices.
Chiara Stevanato, Martin Leijnse, Karsten Flensberg, Jens Paaske Journal reference: Phys. Rev. B 86, 165427 (2012) [pdf] DOI: 10.1103/PhysRevB.86.165427

Hybrid topologicalspin qubit systems for twoqubitspin gates 
Abstract
 We investigate a hybrid quantum system involving spin qubits, based on the spins of electrons confined in quantum dots, and topological qubits, based on Majorana fermions. In such a system, gated control of the charge on the quantum dots allows transfer of quantum information between the spin and topological qubits, and the topological system can be used to facilitate transfer of spin qubits between spatially separated quantum dots and to initialize entangled spinqubit pairs. Here, we show that the coupling to the topological system also makes it possible to perform entangling twoqubit gates on spatially separated spin qubits. The twoqubit gates are based on a combination of topologically protected braiding operations, gatecontrolled charge transfer between the dots and edge Majorana modes, and measurements of the state of the topological qubits.
Martin Leijnse, Karsten Flensberg Journal reference: Phys. Rev. B 86, 104511 (2012) [pdf] DOI: 10.1103/PhysRevB.86.104511

Parallel carbon nanotube quantum dots and their interactions 
Abstract
 We present quantum transport measurements of interacting parallel quantum dots formed in the strands of a carbon nanotube rope. In this molecular quantum dot system, transport is dominated by one quantum dot, while additional resonances from parallel side dots appear, which exhibit a weak gate coupling. This differential gating effect provides a tunability of the quantum dot system with only one gate electrode and provides control over the carbon nanotube strand that carries the current. By tuning the system to different states we use quantum transport as a spectroscopic tool to investigate the interdot coupling and show a route to distinguish between various side dots. By comparing the experimental data with master equation calculations, we identify conditions for the tunneling rates that are required in order to observe different manifestations of the interdot coupling in the transport spectra.
Karin Goß, Martin Leijnse, Sebastian Smerat, Maarten R. Wegewijs, Claus M. Schneider, Carola Meyer [pdf] DOI: 10.1103/PhysRevB.87.035424 1208.5860v1 [pdf]

Emerging Dirac and Majorana fermions for carbon nanotubes with proximityinduced pairing and spiral magnetic field 
Abstract
 We study the lowenergy bandstructure of armchair and smallbandgap semiconducting carbon nanotubes with proximityinduced superconducting pairing when a spiral magnetic field creates strong effective spinorbit interactions from the Zeeman term and a periodic potential from the orbital part. We find that gapless Dirac fermions can be generated by variation of a single parameter. For a semiconducting tube with the field in the same plane, a nondegenerate zero mode at momentum k=0 can be induced, allowing for the generation of topologically protected Majorana fermion end states.
Reinhold Egger, Karsten Flensberg Journal reference: Physical Review B 85, 235462 (2012) [pdf] DOI: 10.1103/PhysRevB.85.235462

Introduction to topological superconductivity and Majorana fermions 
Abstract