Center for Quantum Devices > Research > Publications > QDev publications
Publications by all QDev staff
 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 1808.05837v2 [pdf]

Effective gfactor in Majorana Wires 
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

Antiferromagnetic Order and NonEquilibrium Distributions in the
FloquetEngineered Hubbard Model 
Abstract
 The periodically driven halffilled twodimensional Hubbard model is studied via a saddle point plus fluctuations analysis of the Keldysh action. The drive is implemented as an alternating electric field, and the system is coupled to a metallic substrate in thermal equilibrium to allow for a nonequilibrium steady state synchronized to the drive. For drive frequencies below the equilibrium gap, and strong enough drive amplitudes, the meanfield equation has multiple solutions with a substantial timedependent component. Even for "Magnus" drive frequencies much larger than the equilibrium gap, a oneloop analysis around the meanfield solution shows that even if no real electronhole pairs are excited, the ac drive produces a highly excited, generically nonthermal distribution of fluctuations, which can affect the physics significantly, for example destroying zerotemperature longranged antiferromagnetic order for large enough drive amplitudes.
Nicklas Walldorf, Dante M. Kennes, Jens Paaske, Andrew J. Millis 1809.08607v1 [pdf]

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 1809.07143v1 [pdf]

Topological superconductivity in full shell proximitized 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 1809.05512v1 [pdf]

Fluxinduced Majorana modes 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 1809.05513v1 [pdf]

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

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.

Coulomb blockade of a nearlyopen 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 1809.01660v1 [pdf]

Fast spin exchange between two distant quantum dots 
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).

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) [ 1801.03439v3 ] DOI: 10.1103/PhysRevX.8.031040

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 we show that strong dyonic zeromodes appear when we include suitable positiondependent couplings.
Morten I. Kjærgaard Munk, Asbjørn Rasmussen, Michele Burrello 1807.09286v1 [pdf]

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) [ 1807.05839v1 ] DOI: 10.1103/PhysRevB.98.205403

Hybridization of subgap states in onedimensional
superconductor/semiconductor 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.

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) [ 1802.07808v2 ] DOI: 10.1103/PhysRevMaterials.2.093401

Symmetry analysis of strain, electric and magnetic fields in the
$\text{Bi}_2\text{Se}_3$class of topological insulators 
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 [ 1703.05259v2 ] DOI: 10.1088/13672630/aabcfc

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 1802.01327v1 [pdf]

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) [ 1710.05294v2 ] 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) [ 1712.07972v2 ] DOI: 10.1103/PhysRevB.97.041411

Supercurrent in a double quantum dot 
Abstract
 2017

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) [ 1711.06864v2 ] DOI: 10.1103/PhysRevMaterials.2.044202

Nonlocality of Majorana modes in hybrid nanowires 
Abstract
 Emergent Majorana bound states (MBSs) in topological superconductors appear capable of providing a naturally faulttolerant basis for quantum computing. Key to topological protection is the separation, or nonlocality, of MBSs, which makes Majorana qubits immune to decoherence by a local disturbance. While a number of experiments have reported signatures of MBSs based on zerobias peaks in tunneling conductance, the nonlocal character of Majorana modes  in contrast to Andreev bound states at zero energy  has not been previously demonstrated. Here, we experimentally demonstrate nonlocality of Majorana modes in epitaxial semiconductorsuperconducting nanowires. This is achieved using recent theory showing that nonlocality can be measured via the interaction of the zeroenergy state in the nanowire with a quantumdot state at one end. By comparing coupling to even versus odd occupied quantum dots states, we measure a high degree of nonlocality, consistent with topological MBSs, as well as the spin canting angles of the Majorana modes.
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) [ 1712.03536v1 ] DOI: 10.1103/PhysRevB.98.085125

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) [ 1711.07665v3 ] DOI: 10.1038/s415650180207y

Stability of 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 1712.02789v1 [pdf]

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) [ 1711.06081v1 ] 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) [ 1709.04448v2 ] DOI: 10.1103/PhysRevLett.121.036801

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) [ 1703.03699v2 ] DOI: 10.1103/PhysRevLett.119.176805

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) [ 1710.10012v1 ] DOI: 10.1103/PhysRevX.8.011045

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) [ 1706.07033v2 ] 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) [ 1610.05289v4 ] 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.
Filip Kazimierz Malinowski 1706.03771v1 [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) [ 1706.03587v1 ] 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) [ 1706.01007v1 ] 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) [ 1705.08917v1 ] 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) [ 1612.04852v2 ] 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) [ 1701.01855v2 ] 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) [ 1704.06427v1 ] 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) [ 1606.08458v2 ] 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) [ 1704.01298v1 ] DOI: 10.1103/PhysRevB.96.045443

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) [ 1703.05643v1 ] DOI: 10.1103/PhysRevB.97.060508

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) [ 1601.06677v3 ] 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) [ 1701.01188v1 ] DOI: 10.1038/nphys4224

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) [ 1612.07989v2 ] DOI: 10.1126/science.aaf3961

Engineering hybrid epitaxial InAsSb/Al nanowires for stronger topological protection 
Abstract
 2016

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) [ 1609.01697v2 ] 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) [ 1612.05748v1 ] 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) [ 1608.08769v2 ] 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) [ 1611.10166v1 ] DOI: 10.1021/acs.nanolett.6b04964

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) [ 1603.01852v2 ] 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) [ 1601.01149v4 ] DOI: 10.1103/PhysRevApplied.6.054017

Giant spinorbit splitting in inverted InAs/GaSb double quantum wells 
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) [ 1605.01241v2 ] DOI: 10.1103/PhysRevLett.118.016801

Localization Lifetime of a ManyBody 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 DOI: 10.1002/andp.201600366 1611.05713v1 [pdf]

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) [ 1611.00190v1 ] DOI: 10.1103/PhysRevB.95.035307

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) [ 1602.08926v2 ] 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) [ 1607.08190v2 ] 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) [ 1605.07179v2 ] 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) [ 1605.09385v2 ] 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) [ 1605.02073v2 ] DOI: 10.1103/PhysRevB.94.075439

Quantization of Hall Resistance at the Metallic Interface between an
Oxide Insulator and SrTiO$_{3}$ 
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) [ 1603.02850v2 ] 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) [ 1511.01728v4 ] DOI: 10.1088/13672630/18/8/083005

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) [ 1607.04164v2 ] DOI: 10.1103/PhysRevApplied.7.034029

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) [ 1603.07550v2 ] 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) [ 1606.08470v1 ] 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) [ 1606.08408v1 ] DOI: 10.1103/PhysRevB.94.174514

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) [ 1606.01065v1 ] 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) [ 1601.07369v2 ] 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.
Mark S. Rudner, Michael Levin, Leonid S. Levitov 1605.07652v1 [pdf]

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) [ 1605.01865v1 ] DOI: 10.1038/nnano.2016.227

Evidence of weak superconductivity at the roomtemperature grown
LaAlO$_{3}$/SrTiO$_3$ interface 
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

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

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) [ 1511.05153v2 ] 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) [ 1601.03751v2 ] 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) [ 1602.05039v1 ] 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) [ 1510.05251v2 ] 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

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) [ 1601.06583v1 ] 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) [ 1601.05571v1 ] DOI: 10.1063/1.4935553

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 [ 1601.00628v1 ] DOI: 10.1088/13672630/18/6/065002

Majorana box qubits 
Abstract
 2015

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) [ 1512.09195v1 ] DOI: 10.1103/PhysRevLett.116.150505

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

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

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 DOI: 10.1016/j.physe.2015.08.004 1507.05422v1 [pdf]

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

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

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 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

Gatemon Benchmarking and TwoQubit Operations 
Abstract
 2014

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

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

Magnonic Charge Pumping via SpinOrbit 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 DOI: 10.1038/nnano.2014.252 1411.2779v1 [pdf]

Designing $π$stacked molecular structures to control heat transport
through molecular junctions 
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) [ 1401.0881v1 ] DOI: 10.1103/PhysRevB.89.075417

Tunnel spectroscopy of Majorana bound states in topological superconductor/quantum dot Josephson junctions 
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 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.
N. L. B. Ziino, P. Krogstrup, M. H. Madsen, E. Johnson, J. B. Wagner, C. M. Marcus, J. Nygård, T. S. Jespersen 1309.4569v1 [pdf]

The 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 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

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

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 LongT1 Silicon Nanoparticles for Hyperpolarized 29Si
Magnetic Resonance Imaging 
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 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 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

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

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

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

gTensor Control in Bent Carbon Nanotube Quantum Dots 
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

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

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 DOI: 10.1103/PhysRevB.87.035424 1208.5860v1 [pdf]

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

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

Tunneling Spectroscopy of Quasiparticle Bound States in a Spinful Josephson Junction 
Abstract