Experimental phase diagram of zero-bias conductance peaks in superconductor/semiconductor nanowire devices

Magnetisation control of the nematicity direction and nodal points in a superconducting doped topological insulator

We study the effects of magnetisation on the properties of the doped topological insulator of theBi2Se3family with nematic superconductivity. We found that the direction of the in-plane magnetisation fixes the direction of the nematicity in the system. The chiral state is more favourable than the nematic state for large values of out-of-plane magnetisation. Overall, the critical temperature of the nematic superconductivity is robust against magnetisation. We explore in detail the spectrum of the system with the pinned direction of the nematic order parameterΔy. Without magnetisation, there is a full gap in the spectrum because of finite hexagonal warping. At an out-of-planemzor orthogonal in-planemxmagnetisation that is strong enough, the spectrum is closed at the nodal points that are split by the magnetisation. Flat Majorana surface states connect such split bulk nodal points. Parallel magnetisationmylifts the nodal points and opens a full gap in the spectrum. We discuss relevant experiments and propose experimental verifications of our theory.

Phonon-Assisted Tunneling through Quantum Dot Systems Connected to Majorana Bound States

We theoretically analyze phonon-assisted tunneling transport in a quantum dot side connected to a Majorana bound state in a topological superconducting nanowire. We investigate the behavior of the current through the dot, for a range of experimentally relevant parameters, in the presence of one long-wave optical phonon mode. We consider the current-gate voltage, the current-bias voltage and the current-dot-Majorana coupling characteristics under the influence of the electron-phonon coupling. In the absence of electron-phonon interaction, the Majorana bound states suppress the current when the gate voltage matches the Fermi level, but the increase in the bias voltage counteracts this effect. In the presence of electron-phonon coupling, the current behaves similarly as a function of the renormalized gate voltage. As an added feature at large bias voltages, it presents a dip or a plateau, depending on the size of the dot-Majorana coupling. Lastly, we show that the currents are most sensitive to, and depend non-trivially on the parameters of the Majorana circuit element, in the regime of low temperatures combined with low voltages. Our results provide insights into the complex physics of quantum dot devices used to probe Majorana bound states.

Machine Learning Optimization of Majorana Hybrid Nanowires

As the complexity of quantum systems such as quantum bit arrays increases, efforts to automate expensive tuning are increasingly worthwhile. We investigate machine learning based tuning of gate arrays using the covariance matrix adaptation evolution strategy algorithm for the case study of Majorana wires with strong disorder. We find that the algorithm is able to efficiently improve the topological signatures, learn intrinsic disorder profiles, and completely eliminate disorder effects. For example, with only 20 gates, it is possible to fully recover Majorana zero modes destroyed by disorder by optimizing gate voltages.

Dynamic heat and charge transports through double-quantum-dot-interferometer modulated by Majorana bound states and time-oscillating Aharonov-Bohm flux

Dynamic properties of Majorana bound states (MBSs) coupled double-quantum-dot (DQD) interferometer threaded with ac magnetic flux are investigated, and the time-averaged thermal current formulas are derived. Photon-assisted local and nonlocal Andreev reflections contribute efficiently to the charge and heat transports. The modifications of source-drain electric, electric-thermal, thermal conductances (G,ξ,κ_e), Seebeck coefficient (S_c), and thermoelectric figure of merit (ZT) versus AB phase have been calculated numerically. These coefficients exhibit the shift of oscillation period from 2πto 4πdistinctly due to attaching MBSs. The applied ac flux enhances the magnitudes ofG,ξ,κ_eobviously, and the detailed enhancing behaviors are relevant to the energy levels of DQD. The enhancements ofS_candZTare generated due to the coupling of MBSs, while the application of ac flux suppresses the resonant oscillations. The investigation provides a clue for detecting MBSs through measuring the photon-assistedS_candZTversus AB phase oscillations.

Current through a hybrid four-terminal Josephson junction with Majorana nanowires

We investigate the current through a hybrid four-terminal Josephson junction with semiconductor nanowires, in which the junction is connected with two superconducting electrodes and two normal electrodes. The semiconductor nanowire, which is subject to an external magnetic field with Rashba spin-orbit coupling and proximity-induced superconductivity, can host Majorana bound states. When all the nanowires lie in topological nontrivial region, a 4π-periodic current can be observed through the normal terminal and a 2π-periodic current through the superconducting terminal. When a rotating magnetic field is applied to the junction, the supercurrent through different terminals varies with the variation of the magnetic field direction. Only when the magnetic field is applied at certain angles, we find that the 4π-periodic current will appear through the normal terminal.

Fermion-Parity-Based Computation and Its Majorana-Zero-Mode Implementation

Majorana zero modes (MZMs) promise a platform for topologically protected fermionic quantum computation. However, creating multiple MZMs and generating (directly or via measurements) the requisite transformations (e.g., braids) pose significant challenges. We introduce fermion-parity-based computation (FPBC): a measurement-based scheme, modeled on Pauli-based computation, that uses efficient classical processing to virtually increase the number of available MZMs and which, given magic state inputs, operates without transformations. FPBC requires all MZM parities to be measurable, but this conflicts with constraints in proposed MZM hardware. We thus introduce a design in which all parities are directly measurable and which is hence well suited for FPBC. While developing FPBC, we identify the "logical braid group" as the fermionic analog of the Clifford group.

Universal Conductance Scaling of Andreev Reflections Using a Dissipative Probe

The Majorana search is caught up in an extensive debate about the false-positive signals from nontopological Andreev bound states. We introduce a remedy using the dissipative probe to generate electron-boson interaction. We theoretically show that the interaction-induced renormalization leads to significantly distinct universal zero-bias conductance behaviors, i.e., distinct characteristic power law in temperature, for different types of Andreev reflections, that show a sharp contrast to that of a Majorana zero mode. Various specific cases have been studied, including the cases in which two charges involved in an Andreev reflection process maintain or lose coherence, and the cases for multiple Andreev bound states with or without a Majorana. A transparent list of conductance features in each case is provided to help distinguish the observed subgap states in experiments, which also promotes the identification of Majorana zero modes.

Topological Superconducting Transition Characterized by a Modified Real-Space-Pfaffian Method and Mobility Edges in a One-Dimensional Quasiperiodic Lattice

A modified real-space-Pfaffian method is applied to characterize the topological superconducting transition of a one-dimensional p-wave superconductor with quasiperiodic potentials. We found that the Majorana zero-energy mode exists in the topological non-trivial phase, and its spatial distribution is localized at ends of the system, whereas in the topological trivial phase, there is no Majorana zero mode. Furthermore, we numerically found that due to the competition between the localized quasi-disorder and the extended p-wave pairing, there are mobility edges in the energy spectra. Our theoretical work enriches the research on the quasiperiodic p-wave superconducting models.

Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires

Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhomogeneous wires, the transition between fully-overlapping trivial ABS and nontrivial MBS does not necessarily mandate the closing of the bulk gap of quasiparticle excitations, but a simple parity crossing of partially-separated Majorana modes (ps-MM) from trivial to nontrivial regimes. We demonstrate that fully-separated and fully-overlapping Majorana modes correspond to the two limiting cases at the opposite sides of a continuous crossover: the only distinction between the two can be obtained by estimating the degree of separations of the Majorana components. This result does not contradict the bulk-edge correspondence: indeed, the field inhomogeneities driving the Majorana/Andreev crossover have a length scale comparable with the nanowire length, and therefore correspond to a nonlocal perturbation which breaks the topological protection of the MBS.

Nanoresonator Enhancement of Majorana-Fermion-Induced Slow Light in Superconducting Iron Chains

We theoretically investigate Fano resonance in the absorption spectrum of a quantum dot (QD) based on a hybrid QD-nanomechanical resonator (QD-NR) system mediated by Majorana fermions (MFs) in superconducting iron (Fe) chains. The absorption spectra exhibit a series of asymmetric Fano line shapes, which are accompanied by the rapid normal phase dispersion and induce the optical propagation properties such as the slow light effect under suitable parametric regimes. The results indicated that the slow light induced by MFs can be obtained under different coupling regimes and different detuning regimes. Moreover, we also investigated the role of the NR, and the NR behaving as a phonon cavity enhances the slow light effect.

Sub-gap Fano resonances in a topological superconducting wire with on-site Coulomb interactions

We consider theoretically a 1D-semiconducting wire with strong Rashba interaction in proximity withs-wave superconductor, driven into topological phase by external magnetic field. Additionally, we take into account on-site Coulomb interactions inside the wire. The system is modelled by a tight binding Hamiltonian with Rashba hopping term and induceds-wave superconductivity. Calculations are performed utilizing recursive Green's function method, and Coulomb interactions are treated selfconsistently within Hubbard I approximation. For the Hubbard levels residing withinp-wave superconducting gap, particle-hole symmetric four-resonance structure develops in the density of states, apart from Majorana resonance. One pair of particle-hole symmetric resonances is created by the discrete II-Hubbard levels of the particular site, and the second pair of Hubbard sub-bands originates from recursive summation over the sites of the wire. Quantum interference between both types of pairs of states creates in-gap charge-conjugated Fano resonances with opposite asymmetry factors. We demonstrate that when quantum interference is dominated by two-particle tunneling, the Majorana resonance is strongly diminished, while it is not altered when single-particle tunneling dominates in interference process. We also discuss some consequences for experimental distinction of true Majorana states, and show that on-site Coulomb interactions support the appearance of topological phase.

Shadow-wall lithography of ballistic superconductor-semiconductor quantum devices

The realization of hybrid superconductor-semiconductor quantum devices, in particular a topological qubit, calls for advanced techniques to readily and reproducibly engineer induced superconductivity in semiconductor nanowires. Here, we introduce an on-chip fabrication paradigm based on shadow walls that offers substantial advances in device quality and reproducibility. It allows for the implementation of hybrid quantum devices and ultimately topological qubits while eliminating fabrication steps such as lithography and etching. This is critical to preserve the integrity and homogeneity of the fragile hybrid interfaces. The approach simplifies the reproducible fabrication of devices with a hard induced superconducting gap and ballistic normal-/superconductor junctions. Large gate-tunable supercurrents and high-order multiple Andreev reflections manifest the exceptional coherence of the resulting nanowire Josephson junctions. Our approach enables the realization of 3-terminal devices, where zero-bias conductance peaks emerge in a magnetic field concurrently at both boundaries of the one-dimensional hybrids.

Topological kink states in graphene

Due to the unique band structure, graphene exhibits a number of exotic electronic properties that have not been observed in other materials. Among them, it has been demonstrated that there exist the one-dimensional valley-polarized topological kink states localized in the vicinity of the domain wall of graphene systems, where a bulk energy gap opens due to the inversion symmetry breaking. Notably, the valley-momentum locking nature makes the topological kink states attractive to the property manipulation in valleytronics. This paper systematically reviews both the theoretical research and experimental progress on topological kink states in monolayer graphene, bilayer graphene and graphene-like classical wave systems. Besides, various applications of topological kink states, including the valley filter, current partition, current manipulation, Majorana zero modes and etc, are also introduced.

Parity-preserving and magnetic field-resilient superconductivity in InSb nanowires with Sn shells

Improving materials used to make qubits is crucial to further progress in quantum information processing. Of particular interest are semiconductor-superconductor heterostructures that are expected to form the basis of topological quantum computing. We grew semiconductor indium antimonide nanowires that were coated with shells of tin of uniform thickness. No interdiffusion was observed at the interface between Sn and InSb. Tunnel junctions were prepared by in situ shadowing. Despite the lack of lattice matching between Sn and InSb, a 15-nanometer-thick shell of tin was found to induce a hard superconducting gap, with superconductivity persisting in magnetic field up to 4 teslas. A small island of Sn-InSb exhibits the two-electron charging effect. These findings suggest a less restrictive approach to fabricating superconducting and topological quantum circuits.

Highly Transparent Gatable Superconducting Shadow Junctions

Gate-tunable junctions are key elements in quantum devices based on hybrid semiconductor-superconductor materials. They serve multiple purposes ranging from tunnel spectroscopy probes to voltage-controlled qubit operations in gatemon and topological qubits. Common to all is that junction transparency plays a critical role. In this study, we grow single-crystalline InAs, InSb, and InAs_1-xSb_x semiconductor nanowires with epitaxial Al, Sn, and Pb superconductors and in situ shadowed junctions in a single-step molecular beam epitaxy process. We investigate correlations between fabrication parameters, junction morphologies, and electronic transport properties of the junctions and show that the examined in situ shadowed junctions are of significantly higher quality than the etched junctions. By varying the edge sharpness of the shadow junctions, we show that the sharpest edges yield the highest junction transparency for all three examined semiconductors. Further, critical supercurrent measurements reveal an extraordinarily high I_CR_N, close to the KO-2 limit. This study demonstrates a promising engineering path toward reliable gate-tunable superconducting qubits.

Majorana zero modes in nanowires with combined triangular and hexagonal geometry

The effects of geometry on the hosting of Majorana zero modes are explored in core-shell nanowires with a hexagonal core and a triangular shell, and vice versa. The energy interval separating electronic states localized in the corners from states localized on the sides of the shell is shown to be larger for a triangular nanowire with a hexagonal core, than a triangular one. We build the topological phase diagram for both cases and compare them to earlier work on prismatic nanowires with matching core and shell geometry. We suggest that a dual core nanowire is needed to allow for braiding operations of Majorana zero modes at the nanowire end plane.

General Nanomolding of Ordered Phases

Large-scale, controlled fabrication of ordered phases is challenging at the nanoscale, yet highly demanded as their well-ordered structure and chemistry is the key for advanced functionality. Here, we demonstrate a general nanomolding process of ordered phases based on atomic diffusion. Resulting nanowires are single crystals and maintain their composition and structure throughout their length, which we explain by a self-ordering process originating from their narrow Gibbs free energy. The versatility, control, and precision of this thermomechanical nanomolding method of ordered phases provides new insights into single crystal growth and suggest itself as a technology to enable wide spread usage for nanoscale and quantum devices.

Conductance-Matrix Symmetries of a Three-Terminal Hybrid Device

We present conductance-matrix measurements of a three-terminal superconductor-semiconductor hybrid device consisting of two normal leads and one superconducting lead. Using a symmetry decomposition of the conductance, we find that antisymmetric components of pairs of local and nonlocal conductances qualitatively match at energies below the superconducting gap, and we compare this finding with symmetry relations based on a noninteracting scattering matrix approach. Further, the local charge character of Andreev bound states is extracted from the symmetry-decomposed conductance data and is found to be similar at both ends of the device and tunable with gate voltage. Finally, we measure the conductance matrix as a function of magnetic field and identify correlated splittings in low-energy features, demonstrating how conductance-matrix measurements can complement traditional single-probe measurements in the search for Majorana zero modes.

Supercurrent Detection of Topologically Trivial Zero-Energy States in Nanowire Junctions

We report the emergence of zero-energy states in the trivial phase of a short nanowire junction with a strong spin-orbit coupling and magnetic field, formed by strong coupling between the nanowire and two superconductors. The zero-energy states appear in the junction when the superconductors induce a large energy shift in the nanowire, such that the junction naturally forms a quantum dot, a process that is highly tunable by the superconductor width. Most importantly, we demonstrate that the zero-energy states produce a π shift in the phase-biased supercurrent, which can be used as a simple tool for their unambiguous detection, ruling out any Majorana-like interpretation.

Ubiquitous Non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices

We perform tunneling measurements on indium antimonide nanowire-superconductor hybrid devices fabricated for the studies of Majorana bound states. At finite magnetic field, resonances that strongly resemble Majorana bound states, including zero-bias pinning, become common to the point of ubiquity. Since Majorana bound states are predicted in only a limited parameter range in nanowire devices, we seek an alternative explanation for the observed zero-bias peaks. With the help of a self-consistent Poission-Schrödinger multiband model developed in parallel, we identify several families of trivial subgap states that overlap and interact, giving rise to a crowded spectrum near zero energy and zero-bias conductance peaks in experiments. These findings advance the search for Majorana bound states through improved understanding of broader phenomena found in superconductor-semiconductor systems.

Charge localization and reentrant superconductivity in a quasi-ballistic InAs nanowire coupled to superconductors

A semiconductor nanowire with strong spin-orbit coupling in proximity to a superconductor is predicted to display Majorana edge states emerging under a properly oriented magnetic field. The experimental investigation of these exotic states requires assessing the one-dimensional (1D) character of the nanowire and understanding the superconducting proximity effect in the presence of a magnetic field. Here, we explore the quasi-ballistic 1D transport regime of an InAs nanowire with Ta contacts. Fine-tuned by means of local gates, the observed plateaus of approximately quantized conductance hide the presence of a localized electron, giving rise to a lurking Coulomb blockade effect and Kondo physics. When Ta becomes superconducting, this local charge causes an unusual, reentrant magnetic field dependence of the supercurrent, which we ascribe to a 0 - π transition. Our results underline the relevant role of unintentional charge localization in the few-channel regime where helical subbands and Majorana quasi-particles are expected to arise.

Recent advances in Sb-based III-V nanowires

Owing to the high mobility, narrow bandgap, strong spin-orbit coupling and large g-factor, Sb-based III-V nanowires (NWs) attracted significant interests in high speed electronics, long-wavelength photodetectors and quantum superconductivity in the past decade. In this review, we aim to give an integrated summarization about the recent advances in binary as well as ternary Sb-based III-V NWs, starting from the fundamental properties, NWs growth mechanism, typical synthetic methods to their applications in transistors, photodetectors, and Majorana fermions detection. Up to now, famous NWs growth techniques of solid-source chemical vapor deposition (CVD), molecular beam epitaxy, metal organic vapor phase epitaxy and metal organic CVD etc have been adopted and developed for the controllable growth of Sb-based III-V NWs. Several parameters including heating temperature, III/V ratio of source materials, growth temperature, catalyst size and kinds, and growth substrate play important roles on the morphology, position, diameter distribution, growth orientation and crystal phase of Sb-based III-V NWs. Furthermore, we discuss the photoelectrical applications of Sb-based III-V NWs such as field-effect-transistors, tunnel diode, low-power inverter, and infrared detectors etc. Importantly, due to the strongest spin-orbit interaction and giant g-factor among all III-V semiconductors, InSb with the geometry of one-dimension NW is considered as the most promising candidate for the detection of Majorana fermions. In the end, we also summarize the main challenges remaining in the field and put forward some suggestions for the future development of Sb-based III-V NWs.

Recent advances in III-Sb nanowires: from synthesis to applications

The excellent properties of III-V semiconductors make them intriguing candidates for next-generation electronics and optoelectronics. Their nanowire (NW) counterparts further provide interesting geometry and a quantum confinement effect which benefits various applications. Among the many members of all the III-V semiconductors, III-antimonide NWs have attracted significant research interest due to their narrow, direct bandgap and high carrier mobility. However, due to the difficulty of NW fabrication, the development of III-antimonide NWs and their corresponding applications are always a step behind the other III-V semiconductors. Until recent years, because of advances in understanding and fabrication techniques, electronic and optoelectronic devices based on III-antimonide NWs with novel performance have been fabricated. In this review, we will focus on the development of the synthesis of III-antimonide NWs using different techniques and strategies for fine-tuning the crystal structure and composition as well as fabricating their corresponding heterostructures. With such development, the recent progress in the applications of III-antimonide NWs in electronics and optoelectronics is also surveyed. All these discussions provide valuable guidelines for the design of III-antimonide NWs for next-generation device utilization.

Concomitant opening of a bulk-gap with an emerging possible Majorana zero mode

Majorana quasiparticles are generally detected in a 1D topological superconductor by tunneling electrons into its edge, with an emergent zero-bias conductance peak (ZBCP). However, such a ZBCP can also result from other mechanisms, hence, additional verifications are required. Since the emergence of a Majorana must be accompanied by an opening of a topological gap in the bulk, two simultaneous measurements are performed: one in the bulk and another at the edge of a 1D InAs nanowire coated with epitaxial aluminum. Only under certain experimental parameters, a closing of the superconducting bulk-gap that is followed by its reopening, appears simultaneously with a ZBCP at the edge. Such events suggest the occurrence of a topologically non-trivial phase. Yet, we also find that ZBCPs are observed under different tuning parameters without simultaneous reopening of a bulk-gap. This demonstrates the importance of simultaneous probing of bulk and edge in the identification of Majorana edge-states.

Topological superconductivity in a phase-controlled Josephson junction

Topological superconductors can support localized Majorana states at their boundaries^1-5. These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner^6,7. Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states^8-21. Here we present an experimental approach towards a two-dimensional architecture of Majorana bound states. Using a Josephson junction made of a HgTe quantum well coupled to thin-film aluminium, we are able to tune the transition between a trivial and a topological superconducting state by controlling the phase difference across the junction and applying an in-plane magnetic field²². We determine the topological state of the resulting superconductor by measuring the tunnelling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunnelling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunnelling conductance develops a zero-bias peak, which persists over a range of phase differences that expands systematically with increasing magnetic field. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and probing topological superconducting phases in two-dimensional systems.

Decays of Majorana or Andreev Oscillations Induced by Steplike Spin-Orbit Coupling

The Majorana zero mode in the semiconductor-superconductor nanowire is one of the promising candidates for topological quantum computing. Recently, in islands of nanowires, subgap-state energies have been experimentally observed to oscillate as a function of the magnetic field, showing a signature of overlapped Majorana bound states. However, the oscillation amplitude either dies away after an overshoot or decays, sharply opposite to the theoretically predicted enhanced oscillations for Majorana bound states. We reveal that a steplike distribution of spin-orbit coupling in realistic devices can induce the decaying Majorana oscillations, resulting from the coupling-induced energy repulsion between the quasiparticle spectra on the two sides of the step. This steplike spin-orbit coupling can also lead to decaying oscillations in the spectrum of the Andreev bound states. For Coulomb-blockade peaks mediated by the Majorana bound states, the peak spacings have been predicted to correlate with peak heights by a π/2 phase shift, which was ambiguous in recent experiments and may be explained by the steplike spin-orbit coupling. Our work will inspire more works to reexamine effects of the nonuniform spin-orbit coupling, which is generally present in experimental devices.

Rabi splitting and optical Kerr nonlinearity of quantum dot mediated by Majorana fermions

Majorana fermions (MFs), due to their significance in fundamental physics and potential applications in topological quantum computation based on solid-state devices, have drawn widespread attention. Here, we design a hybrid semiconductor/superconductor ring (S/SR) device and put forward an optical method for detecting a pair of MFs in the S/SR device with a quantum dot (QD) with the popular optical pump-probe scheme, which is very different from the present electrical method only considering one nearby MF coupled to the QD. The symmetric and unsymmetric Rabi splitting and optical Kerr nonlinear effect of QD mediated by MFs are investigated under uncoupled and coupled majorana modes, respectively. The coherent optical spectra indicate that a pair of MFs coupled to the QD induced remarkable splitting under different parameters regime and the physical origin of these phenomena are elaborated detailedly. Due to QD-MFs coupling, the probe absorption spectra present the phenomenon of Majorana modes induced transparency (MMIT) which will induce remarkable phenomena of slow light. The coherent optical spectra afford a potential supplement for probing MFs and support Majorana fermions-based topological quantum computation.

Electron waiting times in hybrid junctions with topological superconductors

We investigate the waiting time distributions (WTDs) of superconducting hybrid junctions, considering both conventional and topologically nontrivial superconductors hosting Majorana bound states at their edges. To this end, we employ a scattering matrix formalism that allows us to evaluate the waiting times between the transmissions and reflections of electrons or holes. Specifically, we analyze normal-metal–superconductor (NIS) junctions and NISIN junctions, where Cooper pairs are spatially split into different leads. The distribution of waiting times is sensitive to the simultaneous reflection of electrons and holes, which is enhanced by the zero-energy state in topological superconductors. For the NISIN junctions, the WTDs of trivial superconductors feature a sharp dependence on the applied voltage, while for topological ones they are mostly independent of it. This particular voltage dependence is again connected to the presence of topological edge states, showing that WTDs are a promising tool for identifying topological superconductivity.

High-Temperature Majorana Corner States

Majorana bound states often occur at the end of a 1D topological superconductor. Validated by a new bulk invariant and an intuitive edge argument, we show the emergence of one Majorana Kramers pair at each corner of a square-shaped 2D topological insulator proximitized by an s_{±}-wave (e.g., Fe-based) superconductor. We obtain a phase diagram that addresses the relaxation of crystal symmetry and edge orientation. We propose two experimental realizations in candidate materials. Our scheme offers a higher-order and higher-temperature route for exploring non-Abelian quasiparticles.

Quasiparticle Interference Studies of Quantum Materials

Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy studies of these surface states have provided a wealth of spectroscopic characterization, with the successful cooperation of ab initio calculations. The method of quasiparticle interference imaging proves to be particularly useful for probing the dispersion relation of the surface bands. Herein, how a variety of additional fundamental electronic properties can be probed via this method is reviewed. It is demonstrated how quasiparticle interference measurements entail mesoscopic size quantization and the electronic phase coherence in semiconducting nanowires; helical spin protection and energy-momentum fluctuations in a topological insulator; and the structure of the Bloch wave function and the relative insusceptibility of topological electronic states to surface potential in a topological Weyl semimetal.

Mirage Andreev Spectra Generated by Mesoscopic Leads in Nanowire Quantum Dots

We study transport mediated by Andreev bound states formed in InSb nanowire quantum dots. Two kinds of superconducting source and drain contacts are used: epitaxial Al/InSb devices exhibit a doubling of tunneling resonances, while, in NbTiN/InSb devices, Andreev spectra of the dot appear to be replicated multiple times at increasing source-drain bias voltages. In both devices, a mirage of a crowded spectrum is created. To describe the observations a model is developed that combines the effects of a soft induced gap and of additional Andreev bound states both in the quantum dot and in the finite regions of the nanowire adjacent to the quantum dot. Understanding of Andreev spectroscopy is important for the correct interpretation of Majorana experiments done on the same structures.

Hidden chiral symmetries in BDI multichannel Kitaev chains

Realistic implementations of the Kitaev chain require, in general, the introduction of extra internal degrees of freedom. In the present work, we discuss the presence of hidden BDI symmetries for free Hamiltonians describing systems with an arbitrary number of internal degrees of freedom. We generalize results of a spinfull Kitaev chain to construct a Hamiltonian with n internal degrees of freedom and obtain the corresponding hidden chiral symmetry. As an explicit application of this generalized result, we exploit by analytical and numerical calculations the case of a spinful two-band Kitaev chain, which can host up to four Majorana bound states. We also observe the appearence of minigap states, when chiral symmetry is broken.

Ballistic Majorana nanowire devices

Majorana modes are zero-energy excitations of a topological superconductor that exhibit non-Abelian statistics1-3. Following proposals for their detection in a semiconductor nanowire coupled to an s-wave superconductor4,5, several tunnelling experiments reported characteristic Majorana signatures6-11. Reducing disorder has been a prime challenge for these experiments because disorder can mimic the zero-energy signatures of Majoranas12-16, and renders the topological properties inaccessible17-20. Here, we show characteristic Majorana signatures in InSb nanowire devices exhibiting clear ballistic transport properties. Application of a magnetic field and spatial control of carrier density using local gates generates a zero bias peak that is rigid over a large region in the parameter space of chemical potential, Zeeman energy and tunnel barrier potential. The reduction of disorder allows us to resolve separate regions in the parameter space with and without a zero bias peak, indicating topologically distinct phases. These observations are consistent with the Majorana theory in a ballistic system 21 , and exclude the known alternative explanations that invoke disorder12-16 or a nonuniform chemical potential22,23.

Robust topological phase in proximitized core-shell nanowires coupled to multiple superconductors

We consider core-shell nanowires with prismatic geometry contacted with two or more superconductors in the presence of a magnetic field applied parallel to the wire. In this geometry, the lowest energy states are localized on the outer edges of the shell, which strongly inhibits the orbital effects of the longitudinal magnetic field that are detrimental to Majorana physics. Using a tight-binding model of coupled parallel chains, we calculate the topological phase diagram of the hybrid system in the presence of non-vanishing transverse potentials and finite relative phases between the parent superconductors. We show that having finite relative phases strongly enhances the stability of the induced topological superconductivity over a significant range of chemical potentials and reduces the value of the critical field associated with the topological quantum phase transition.

Supercurrent Interference in Few-Mode Nanowire Josephson Junctions

Junctions created by coupling two superconductors via a semiconductor nanowire in the presence of high magnetic fields are the basis for the potential detection, fusion, and braiding of Majorana bound states. We study NbTiN/InSb nanowire/NbTiN Josephson junctions and find that the dependence of the critical current on the magnetic field exhibits gate-tunable nodes. This is in contrast with a well-known Fraunhofer effect, under which critical current nodes form a regular pattern with a period fixed by the junction area. Based on a realistic numerical model we conclude that the Zeeman effect induced by the magnetic field and the spin-orbit interaction in the nanowire are insufficient to explain the observed evolution of the Josephson effect. We find the interference between the few occupied one-dimensional modes in the nanowire to be the dominant mechanism responsible for the critical current behavior. We also report a strong suppression of critical currents at finite magnetic fields that should be taken into account when designing circuits based on Majorana bound states.