Enhanced Majorana stability in a three-site Kitaev chain

Majorana zero modes are non-Abelian quasiparticles predicted to emerge at the edges of topological superconductors. A one-dimensional topological superconductor can be realized with the Kitaev model-a chain of spinless fermions coupled via p-wave superconductivity and electron hopping-which becomes topological in the long-chain limit. Here we realize a three-site Kitaev chain using semiconducting quantum dots coupled by superconducting segments in a hybrid InSb/Al nanowire. We investigate the robustness of Majorana zero modes under varying coupling strengths and electrochemical potentials, comparing two- and three-site chains realized within the same device. We observe that extending the chain to three sites enhances the stability of the zero-energy modes, especially against variations in the coupling strengths. This experiment lacks superconducting phase control, yet numerical conductance simulations with phase averaging align well with our observations. Our results demonstrate the scalability of quantum-dot-based Kitaev chains and its benefits for Majorana stability.

Dressed Majorana Fermion in a Hybrid Nanowire

In hybrid systems where nanowires are proximity-coupled with superconductors, the low-energy theory fails to determine the topological phase with Majorana fermion (MF) when the magnetic field or proximity coupling is much stronger. To overcome this limitation, we propose a holistic approach that defines MF by considering both the motion of electrons in the nanowire and the quasiparticle excitations in the superconductor. This approach transcends the constraints of low-energy theory and offers broad applicability. Our approach reveals that the topological phase diagram depends not only on the chemical potential and Zeeman energy in the nanowire, but also on those in the superconductor, and the matched chemical potentials are more favorable for observing MF. This broader perspective provides specific experimental guidance under various conditions.

Flexible Control of Chiral Superconductivity in Optically Driven Nodal Point Superconductors with Antiferromagnetism

Recent studies have attracted widespread attention on magnet-superconductor hybrid systems with emergent topological superconductivity. Here, we present the Floquet engineering of realistic two-dimensional topological nodal-point superconductors that are composed of antiferromagnetic monolayers in proximity to an s-wave superconductor. We show that Floquet chiral topological superconductivity arises due to light-induced breaking of the effective time-reversal symmetry. More strikingly, we find that the Floquet chiral topological superconducting phases can be flexibly controlled by irradiating elliptically polarized light, with the photon-dressed quasienergy spectrum carrying different Chern numbers. Such optically switchable topological transitions arise from the simultaneous creations (or annihilations) of valley pairs, which are attributed to the intertwining with magnetic symmetry, superconductivity, and topology. Our findings provide a feasible approach for achieving the Floquet chiral topological superconductivity with flexible tunability, which would draw extensive attention in experiments.

Topological superconductivity from unconventional band degeneracy with conventional pairing

We present a new scheme for Majorana modes in systems with nonsymmorphic-symmetry-protected band degeneracy. We reveal that when the gapless fermionic excitations are encoded with conventional superconductivity and magnetism, which can be intrinsic or induced by proximity effect, topological superconductivity and Majorana modes can be obtained. We illustrate this outcome in a system which respects the space group P4/nmm and features a fourfold-degenerate fermionic mode at (π,  π) in the Brillouin zone. We show that in the presence of conventional superconductivity, different types of topological superconductivity, i.e., first-order and second-order topological superconductivity, with coexisting fragile Wannier obstruction in the latter case, can be generated in accordance with the different types of magnetic orders; Majorana modes are shown to exist on the boundary, at the corner and in the vortices. To further demonstrate the effectiveness of our approach, another example related to the space group P4/ncc based on this scheme is also provided. Our study offers insights into constructing topological superconductors based on bulk energy bands and conventional superconductivity and helps to find new material candidates and design new platforms for realizing Majorana modes.

Altermagnetic Routes to Majorana Modes in Zero Net Magnetization

We propose heterostructures that realize first and second order topological superconductivity with vanishing net magnetization by utilizing altermagnetism. Such platforms may offer a significant improvement over conventional platforms with uniform magnetization since the latter suppresses the superconducting gap. We first introduce a 1D semiconductor-superconductor structure in proximity to an altermagnet that realizes end Majorana zero modes (MZMs) with vanishing net magnetization. Additionally, a coexisting Zeeman term provides a tuning knob to distinguish topological and trivial zero modes. We then propose 2D altermagnetic platforms that can realize chiral Majorana fermions or higher order corner MZMs. Our Letter paves the way toward realizing Majorana boundary states with an alternative source of time-reversal breaking and zero net magnetization.

Versatile Method of Engineering the Band Alignment and the Electron Wavefunction Hybridization of Hybrid Quantum Devices

Hybrid devices that combine superconductors (S) and semiconductors (Sm) have attracted great attention due to the integration of the properties of both materials, which relies on the interface details and the resulting coupling strength and wavefunction hybridization. However, until now, none of the experiments have reported good control of the band alignment of the interface, as well as its tunability to the coupling and hybridization. Here, the interface is modified by inducing specific argon milling while maintaining its high quality, e.g., atomic connection, which results in a large induced superconducting gap and ballistic transport. By comparing with Schrödinger-Poisson calculations, it is proven that this method can vary the band bending/coupling strength and the electronic spatial distribution. In the strong coupling regime, the coexistence and tunability of crossed Andreev reflection and elastic co-tunneling-key ingredients for the Kitaev chain-are confirmed. This method is also generic for other materials and achieves a hard and huge superconducting gap in lead and indium antimonide nanowire (Pb-InSb) devices. Such a versatile method, compatible with the standard fabrication process and accompanied by the well-controlled modification of the interface, will definitely boost the creation of more sophisticated hybrid devices for exploring physics in solid-state systems.

Heat Dissipation Mechanisms in Hybrid Superconductor-Semiconductor Devices Revealed by Joule Spectroscopy

Understanding heating and cooling mechanisms in mesoscopic superconductor-semiconductor devices is crucial for their application in quantum technologies. Owing to their poor thermal conductivity, heating effects can drive superconducting-to-normal transitions even at low bias, observed as sharp conductance dips through the loss of Andreev excess currents. Tracking such dips across magnetic field, cryostat temperature, and applied microwave power allows us to uncover cooling bottlenecks in different parts of a device. By applying this "Joule spectroscopy" technique, we analyze heat dissipation in devices based on InAs-Al nanowires and reveal that cooling of superconducting islands is limited by the rather inefficient electron-phonon coupling, as opposed to grounded superconductors that primarily cool by quasiparticle diffusion. We show that powers as low as 50-150 pW are able to suppress superconductivity on the islands. Applied microwaves lead to similar heating effects but are affected by the interplay of the microwave frequency and the effective electron-phonon relaxation time.

Hunting for Majoranas

Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.

Joule spectroscopy of hybrid superconductor-semiconductor nanodevices

Hybrid superconductor-semiconductor devices offer highly tunable platforms, potentially suitable for quantum technology applications, that have been intensively studied in the past decade. Here we establish that measurements of the superconductor-to-normal transition originating from Joule heating provide a powerful spectroscopical tool to characterize such hybrid devices. Concretely, we apply this technique to junctions in full-shell Al-InAs nanowires in the Little-Parks regime and obtain detailed information of each lead independently and in a single measurement, including differences in the superconducting coherence lengths of the leads, inhomogeneous covering of the epitaxial shell, and the inverse superconducting proximity effect; all-in-all constituting a unique fingerprint of each device with applications in the interpretation of low-bias data, the optimization of device geometries, and the uncovering of disorder in these systems. Besides the practical uses, our work also underscores the importance of heating in hybrid devices, an effect that is often overlooked.

Non-Destructive Low-Temperature Contacts to MoS2 Nanoribbon and Nanotube Quantum Dots

Molybdenum disulfide nanoribbons and nanotubes are quasi-1D semiconductors with strong spin-orbit interaction, a nanomaterial highly promising for quantum electronic applications. Here, it is demonstrated that a bismuth semimetal layer between the contact metal and this nanomaterial strongly improves the properties of the contacts. Two-point resistances on the order of 100 kΩ are observed at room temperature. At cryogenic temperature, Coulomb blockade is visible. The resulting stability diagrams indicate a marked absence of trap states at the contacts and the corresponding disorder, compared to previous devices that use low-work-function metals as contacts. Single-level quantum transport is observed at temperatures below 100 mK.

Realization of a minimal Kitaev chain in coupled quantum dots

Majorana bound states constitute one of the simplest examples of emergent non-Abelian excitations in condensed matter physics. A toy model proposed by Kitaev shows that such states can arise at the ends of a spinless p-wave superconducting chain¹. Practical proposals for its realization^2,3 require coupling neighbouring quantum dots (QDs) in a chain through both electron tunnelling and crossed Andreev reflection⁴. Although both processes have been observed in semiconducting nanowires and carbon nanotubes^5-8, crossed-Andreev interaction was neither easily tunable nor strong enough to induce coherent hybridization of dot states. Here we demonstrate the simultaneous presence of all necessary ingredients for an artificial Kitaev chain: two spin-polarized QDs in an InSb nanowire strongly coupled by both elastic co-tunnelling (ECT) and crossed Andreev reflection (CAR). We fine-tune this system to a sweet spot where a pair of poor man's Majorana states is predicted to appear. At this sweet spot, the transport characteristics satisfy the theoretical predictions for such a system, including pairwise correlation, zero charge and stability against local perturbations. Although the simple system presented here can be scaled to simulate a full Kitaev chain with an emergent topological order, it can also be used imminently to explore relevant physics related to non-Abelian anyons.

Majorana-like Coulomb spectroscopy in the absence of zero-bias peaks

Hybrid semiconductor-superconductor devices hold great promise for realizing topological quantum computing with Majorana zero modes1-5. However, multiple claims of Majorana detection, based on either tunnelling6-10 or Coulomb blockade (CB) spectroscopy11,12, remain disputed. Here we devise an experimental protocol that allows us to perform both types of measurement on the same hybrid island by adjusting its charging energy via tunable junctions to the normal leads. This method reduces ambiguities of Majorana detections by checking the consistency between CB spectroscopy and zero-bias peaks in non-blockaded transport. Specifically, we observe junction-dependent, even-odd modulated, single-electron CB peaks in InAs/Al hybrid nanowires without concomitant low-bias peaks in tunnelling spectroscopy. We provide a theoretical interpretation of the experimental observations in terms of low-energy, longitudinally confined island states rather than overlapping Majorana modes. Our results highlight the importance of combined measurements on the same device for the identification of topological Majorana zero modes.

Electronic Transport in Double-Nanowire Superconducting Islands with Multiple Terminals

We characterize in situ grown parallel nanowires bridged by a superconducting island. The magnetic-field and temperature dependence of Coulomb blockade peaks measured across different pairs of nanowire ends suggest the presence of a subgap state extended over the hybrid parallel-nanowire island. Being gate-tunable, accessible by multiple terminals, and free of quasiparticle poisoning, these nanowires show promise for the implementation of several proposals that rely on parallel nanowire platforms.

Readout of Parafermionic States by Transport Measurements

Recent experiments have demonstrated the possibility of inducing superconducting pairing into counterpropagating fractional quantum Hall edge modes. This paves the way for the realization of localized parafermionic modes, non-Abelian anyons that share fractional charges in a nonlocal way. We show that, for a pair of isolated parafermions, this joint degree of freedom can be read by conductance measurements across standard metallic electrodes. We propose two complementary setups. We investigate first the transport through a grounded superconductor hosting two interacting parafermions. In the low-energy limit, its conductance peaks reveal their shared fractional charge yielding a three-state telegraph noise for weak quasiparticle poisoning. We then examine the two-terminal electron conductance of a blockaded fractional topological superconductor, which displays a characteristic e/3 periodicity of its zero-bias peaks in the deep topological regime, thus signaling the presence of parafermionic modes.

Electrically tunable spin-orbit interaction in an InAs nanosheet

We report an experimental study of the spin-orbit interaction (SOI) in an epitaxially grown free-standing InAs nanosheet in a dual-gate field-effect device. Gate-transfer characteristic measurements show that independent tuning of the carrier density in the nanosheet and the potential difference across the nanosheet can be efficiently achieved with the use of a dual gate. The quantum transport characteristics of the InAs nanosheet are investigated by magnetoconductance measurements at low temperatures. It is shown that the electron transport in the nanosheet can be tuned from the weak antilocalization to the weak localization and then back to the weak antilocalization regime with a voltage applied over the dual gate without a change in the carrier density. The spin-orbit length extracted from the magnetoconductance measurements at a constant carrier density exhibits a peak value at which the SOI of the Rashba type is suppressed and the spin relaxation due to the presence of an SOI of the Dresselhaus type in the nanosheet can be revealed. Energy band diagram simulations have also been carried out for the device under the experimental conditions and the physical insights into the experimental observations have been discussed in light of the results of simulations.

Excitations in a superconducting Coulombic energy gap

Cooper pairing and Coulomb repulsion are antagonists, producing distinct energy gaps in superconductors and Mott insulators. When a superconductor exchanges unpaired electrons with a quantum dot, its gap is populated by a pair of electron-hole symmetric Yu-Shiba-Rusinov excitations between doublet and singlet many-body states. The fate of these excitations in the presence of a strong Coulomb repulsion in the superconductor is unknown, but of importance in applications such as topological superconducting qubits and multi-channel impurity models. Here we couple a quantum dot to a superconducting island with a tunable Coulomb repulsion. We show that a strong Coulomb repulsion changes the singlet many-body state into a two-body state. It also breaks the electron-hole energy symmetry of the excitations, which thereby lose their Yu-Shiba-Rusinov character.

Heat-Mode Excitation in a Proximity Superconductor

Mesoscopic superconductivity deals with various quasiparticle excitation modes, only one of them-the charge-mode-being directly accessible for conductance measurements due to the imbalance in populations of quasi-electron and quasihole excitation branches. Other modes carrying heat or even spin, valley etc. currents populate the branches equally and are charge-neutral, which makes them much harder to control. This noticeable gap in the experimental studies of mesoscopic non-equilibrium superconductivity can be filled by going beyond the conventional DC transport measurements and exploiting spontaneous current fluctuations. Here, we perform such an experiment and investigate the transport of heat in an open hybrid device based on a superconductor proximitized InAs nanowire. Using shot noise measurements, we investigate sub-gap Andreev heat guiding along the superconducting interface and fully characterize it in terms of the thermal conductance on the order of Gth∼e2/h, tunable by a back gate voltage. Understanding of the heat-mode also uncovers its implicit signatures in the non-local charge transport. Our experiments open a direct pathway to probe generic charge-neutral excitations in superconducting hybrids.

Sachdev-Ye-Kitaev Circuits for Braiding and Charging Majorana Zero Modes

The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. Here we construct fermionic all-to-all Floquet quantum circuits of random four-body gates designed to capture key features of SYK dynamics. Our circuits can be built using local ingredients in Majorana devices, namely, charging-mediated interactions and braiding Majorana zero modes. This offers an analog-digital route to SYK quantum simulations that reconciles all-to-all interactions with the topological protection of Majorana zero modes, a key feature missing in existing proposals for analog SYK simulation. We also describe how dynamical, including out-of-time-ordered, correlation functions can be measured in such analog-digital implementations by employing foreseen capabilities in Majorana devices.

Andreev Interference in the Surface Accumulation Layer of Half-Shell InAsSb/Al Hybrid Nanowires

Understanding the spatial distribution of charge carriers in III-V nanowires proximity coupled to superconductors is important for the design and interpretation of experiments based on hybrid quantum devices. In this letter, the gate-dependent surface accumulation layer of half-shell InAsSb/Al nanowires is studied by means of Andreev interference in a parallel magnetic field. Both uniform hybrid nanowires and devices featuring a short Josephson junction fabricated by shadow lithography, exhibit periodic modulation of the switching current. The period corresponds to a flux quantum through the nanowire diameter and is consistent with Andreev bound states occupying a cylindrical surface accumulation layer. The spatial distribution is tunable by a gate potential as expected from electrostatic 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.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Sub-Band Spectrum Engineering via Structural Order in Tapered Nanowires

The cross-sectional dimensions of nanowires set the quantization conditions for the electronic subbands they host. These can be used as a platform to realize one-dimesional topological superconductivity. Here we develop a protocol that forces such nanowires to kink and change their growth direction. Consequently, a thin rectangular nanoplate is formed, which gradually converges into a very thin square tip. We characterize the resulting tapered nanowires structurally and spectroscopically by scanning and transmission electron microscopy and scanning tunneling microscopy and spectroscopy and model their growth. A unique structure composed of ordered rows of atoms on the (110) facet of the nanoflag is further revealed by atomically resolved topography and modeled by simulations. We discuss possible advantages tapered InAs nanowires offer for Majorana zero-mode realization and manipulation.

Superconductivity and Parity Preservation in As-Grown In Islands on InAs Nanowires

We report in situ synthesis of crystalline indium islands on InAs nanowires grown by molecular beam epitaxy. Structural analysis by transmission electron microscopy showed that In crystals grew in a tetragonal body-centered crystal structure within two families of orientations relative to wurtzite InAs. The crystalline islands had lengths < 500 nm and low-energy surfaces, suggesting that growth was driven mainly by surface energy minimization. Electrical transport through In/InAs devices exhibited Cooper pair charging, evidencing charge parity preservation and a pristine In/InAs interface, with an induced superconducting gap ∼ 0.45 meV. Cooper pair charging persisted to temperatures > 1.2 K and magnetic fields ∼ 0.7 T, demonstrating that In/InAs hybrids belong to an expanding class of semiconductor/superconductor hybrids operating over a wider parameter space than state-of-the-art Al-based hybrids. Engineering crystal morphology while isolating single islands using shadow epitaxy provides an interesting alternative to previous semiconductor/superconductor hybrid morphologies and device geometries.

Andreev Molecule in Parallel InAs Nanowires

Coupling individual atoms fundamentally changes the state of matter: electrons bound to atomic cores become delocalized turning an insulating state to a metallic one. A chain of atoms could lead to more exotic states if the tunneling takes place via the superconducting vacuum and can induce topologically protected excitations like Majorana or parafermions. Although coupling a single atom to a superconductor is well studied, the hybridization of two sites with individual tunability was not reported yet. The peculiar vacuum of the Bardeen-Cooper-Schrieffer (BCS) condensate opens the way to annihilate or generate two electrons from the bulk resulting in a so-called Andreev molecular state. By employing parallel nanowires with an Al shell, two artificial atoms were created at a minimal distance with an epitaxial superconducting link between. Hybridization via the BCS vacuum was observed and the spectrum of an Andreev molecule as a function of level positions was explored for the first time.

Magnetization Signature of Topological Surface States in a Non-Symmorphic Superconductor

Superconductors with nontrivial band structure topology represent a class of materials with unconventional and potentially useful properties. Recent years have seen much success in creating artificial hybrid structures exhibiting the main characteristics of 2D topological superconductors. Yet, bulk materials known to combine inherent superconductivity with nontrivial topology remain scarce, largely because distinguishing their central characteristic-the topological surface states-has proved challenging due to a dominant contribution from the superconducting bulk. In this work, a highly anomalous behavior of surface superconductivity in topologically nontrivial 3D superconductor In2 Bi, where the surface states result from its nontrivial band structure, itself a consequence of the non-symmorphic crystal symmetry and strong spin-orbit coupling, is reported. In contrast to smoothly decreasing diamagnetic susceptibility above the bulk critical field, Hc2 , as seen in conventional superconductors, a near-perfect, Meissner-like screening of low-frequency magnetic fields well above Hc2 is observed. The enhanced diamagnetism disappears at a new phase transition close to the critical field of surface superconductivity, Hc3 . Using theoretical modeling, the anomalous screening is shown to be consistent with modification of surface superconductivity by the topological surface states. The possibility of detecting signatures of the surface states using macroscopic magnetization provides a new tool for the discovery and identification of topological superconductors.

Asymmetric Little-Parks oscillations in full shell double nanowires

Little-Parks oscillations of a hollow superconducting cylinder are of interest for flux-driven topological superconductivity in single Rashba nanowires. The oscillations are typically symmetric in the orientation of the applied magnetic flux. Using double InAs nanowires coated by an epitaxial superconducting Al shell which, despite the non-centro-symmetric geometry, behaves effectively as one hollow cylinder, we demonstrate that a small misalignment of the applied parallel field with respect to the axis of the nanowires can produce field-asymmetric Little-Parks oscillations. These are revealed by the simultaneous application of a magnetic field perpendicular to the misaligned parallel field direction. The asymmetry occurs in both the destructive regime, in which superconductivity is destroyed for half-integer quanta of flux through the shell, and in the non-destructive regime, where superconductivity is depressed but not fully destroyed at these flux values.

Tuning Electronic Properties of 2D Materials Using Metal Adsorbates: Cu at WTe2 Edges

Two-dimensional materials exhibit properties promising for novel applications. Topologically protected states at their edges can be harnessed for use in quantum devices. We use ab initio simulations to examine properties of edges in 1T'-WTe₂ monolayers, known to exhibit topological order, and their interactions with Cu atoms. Comparison of (010)-oriented edges that have the same composition but different terminations shows that, as the number of Cu atoms increases, their thermodynamically preferred arrangement depends on the details of the edge structure. Cu atoms aggregate into a cluster at the most stable edge; while the cluster is nonmagnetic, it spin-polarizes the W atoms along the edge, which removes the topological protection. At the metastable edge, Cu atoms form a chain incorporated into the WTe₂ lattice; the topological state is preserved in spite of the dramatic edge restructuring. This suggests that exploiting interactions of metal species with metastable edge terminations can provide a path toward noninvasive interfaces.

Nontopological zero-bias peaks in full-shell nanowires induced by flux-tunable Andreev states

A semiconducting nanowire fully wrapped by a superconducting shell has been proposed as a platform for obtaining Majorana modes at small magnetic fields. In this study, we demonstrate that the appearance of subgap states in such structures is actually governed by the junction region in tunneling spectroscopy measurements and not the full-shell nanowire itself. Short tunneling regions never show subgap states, whereas longer junctions always do. This can be understood in terms of quantum dots forming in the junction and hosting Andreev levels in the Yu-Shiba-Rusinov regime. The intricate magnetic field dependence of the Andreev levels, through both the Zeeman and Little-Parks effects, may result in robust zero-bias peaks-features that could be easily misinterpreted as originating from Majorana zero modes but are unrelated to topological superconductivity.

Epitaxial Pb on InAs nanowires for quantum devices

Semiconductor-superconductor hybrids are widely used to realize complex quantum phenomena, such as topological superconductivity and spins coupled to Cooper pairs. Accessing new, exotic regimes at high magnetic fields and increasing operating temperatures beyond the state-of-the-art requires new, epitaxially matched semiconductor-superconductor materials. One challenge is the generation of favourable conditions for heterostructural formation between materials with the desired properties. Here we harness an increased knowledge of metal-on-semiconductor growth to develop InAs nanowires with epitaxially matched, single-crystal, atomically flat Pb films with no axial grain boundaries. These highly ordered heterostructures have a critical temperature of 7 K and a superconducting gap of 1.25 meV, which remains hard at 8.5 T, and therefore they offer a parameter space more than twice as large as those of alternative semiconductor-superconductor hybrids. Additionally, InAs/Pb island devices exhibit magnetic field-driven transitions from a Cooper pair to single-electron charging, a prerequisite for use in topological quantum computation. Semiconductor-Pb hybrids potentially enable access to entirely new regimes for a number of different quantum systems.

Phase-induced topological superconductivity in a planar heterostructure

Topological superconductivity in quasi-one-dimensional systems is a novel phase of matter with possible implications for quantum computation. Despite years of effort, a definitive signature of this phase in experiments is still debated. A major cause of this ambiguity is the side effects of applying a magnetic field: induced in-gap states, vortices, and alignment issues. Here we propose a planar semiconductor-superconductor heterostructure as a platform for realizing topological superconductivity without applying a magnetic field to the two-dimensional electron gas hosting the topological state. Time-reversal symmetry is broken only by phase biasing the proximitizing superconductors, which can be achieved using extremely small fluxes or bias currents far from the quasi-one-dimensional channel. Our platform is based on interference between this phase biasing and the phase arising from strong spin-orbit coupling in closed electron trajectories. The principle is demonstrated analytically using a simple model, and then shown numerically for realistic devices. We show a robust topological phase diagram, as well as explicit wavefunctions of Majorana zero modes. We discuss experimental issues regarding the practical implementation of our proposal, establishing it as an accessible scheme with contemporary experimental techniques.

Low-energy in-gap states of vortices in superconductor-semiconductor heterostructures

The recent interest in the low-energy states in vortices of semiconductor-superconductor heterostructures are mainly fuelled by the prospects of using Majorana zero modes for quantum computation. The knowledge of low-lying states in the vortex core is essential as they pose a limitation on the topological computation with these states. Recently, the low-energy spectra of clean heterostructures, for superconducting-pairing profiles that vary slowly on the scale of the Fermi wavelength of the semiconductor, have been analytically calculated. In this work, we formulate an alternative method based on perturbation theory to obtain concise analytical formulas to predict the low-energy states including explicit magnetic-field and gap profiles. We provide results for both a topological insulator (with a linear spectrum) as well as for a conventional electron gas (with a quadratic spectrum). We discuss the spectra for a wide range of parameters, including both the size of the vortex and the chemical potential of the semiconductor, and thereby provide a tool to guide future experimental efforts. We compare these findings to numerical results.

Quasiparticle Poisoning of Majorana Qubits

Qubits based on Majorana zero modes are a promising path towards topological quantum computing. Such qubits, though, are susceptible to quasiparticle poisoning which does not have to be small by topological argument. We study the main sources of the quasiparticle poisoning relevant for realistic devices-nonequilibrium above-gap quasiparticles and equilibrium localized subgap states. Depending on the parameters of the system and the architecture of the qubit either of these sources can dominate the qubit decoherence. However, we find in contrast to naive estimates that in moderately disordered, floating Majorana islands the quasiparticle poisoning can have timescales exceeding seconds.

Andreev Modes from Phase Winding in a Full-Shell Nanowire-Based Transmon

We investigate transmon qubits made from semiconductor nanowires with a fully surrounding superconducting shell. In the regime of reentrant superconductivity associated with the destructive Little-Parks effect, numerous coherent transitions are observed in the first reentrant lobe, where the shell carries 2π winding of superconducting phase, and are absent in the zeroth lobe. As junction density was increased by gate voltage, qubit coherence was suppressed then lost in the first lobe. These observations and numerical simulations highlight the role of winding-induced Andreev states in the junction.

Fragility of the Fractional Josephson Effect in Time-Reversal-Invariant Topological Superconductors

Time-reversal-invariant topological superconductor (TRITOPS) wires host Majorana Kramers pairs that have been predicted to mediate a fractional Josephson effect with 4π periodicity in the superconducting phase difference. We explore the TRITOPS fractional Josephson effect in the presence of time-dependent "local mixing" perturbations that instantaneously preserve time-reversal symmetry. Specifically, we show that just as such couplings render braiding of Majorana Kramers pairs nonuniversal, the Josephson current becomes either aperiodic or 2π periodic (depending on conditions that we quantify) unless the phase difference is swept sufficiently quickly. We further analyze topological superconductors with T^{2}=+1 time-reversal symmetry and reveal a rich interplay between interactions and local mixing that can be experimentally probed in nanowire arrays.

Destructive Little-Parks Effect in a Full-Shell Nanowire-Based Transmon

A semiconductor transmon with an epitaxial Al shell fully surrounding an InAs nanowire core is investigated in the low E_{J}/E_{C} regime. Little-Parks oscillations as a function of flux along the hybrid wire axis are destructive, creating lobes of reentrant superconductivity separated by a metallic state at a half quantum of applied flux. In the first lobe, phase winding around the shell can induce topological superconductivity in the core. Coherent qubit operation is observed in both the zeroth and first lobes. Splitting of parity bands by coherent single-electron coupling across the junction is not resolved beyond line broadening, placing a bound on Majorana coupling, E_{M}/h<10  MHz, much smaller than the Josephson coupling E_{J}/h∼4.7  GHz.

Quantum Dot Parity Effects in Trivial and Topological Josephson Junctions

An odd-occupied quantum dot in a Josephson junction can flip transmission phase, creating a π junction. When the junction couples topological superconductors, no phase flip is expected. We investigate this and related effects in a full-shell hybrid interferometer, using gate voltage to control dot-junction parity and axial magnetic flux to control the transition from trivial to topological superconductivity. Enhanced zero-bias conductance and critical current for odd parity in the topological phase reflects hybridization of the confined spin with zero-energy modes in the leads.

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.

Shadow Epitaxy for In Situ Growth of Generic Semiconductor/Superconductor Hybrids

Uniform, defect-free crystal interfaces and surfaces are crucial ingredients for realizing high-performance nanoscale devices. A pertinent example is that advances in gate-tunable and topological superconductivity using semiconductor/superconductor electronic devices are currently built on the hard proximity-induced superconducting gap obtained from epitaxial indium arsenide/aluminum heterostructures. Fabrication of devices requires selective etch processes; these exist only for InAs/Al hybrids, precluding the use of other, potentially superior material combinations. This work introduces a crystal growth platform-based on 3D structuring of growth substrates-which enables synthesis of semiconductor nanowire hybrids with in situ patterned superconductor shells. The platform eliminates the need for etching, thereby enabling full freedom in the choice of hybrid constituents. All of the most frequently used superconducting hybrid device architectures are realized and characterized. These devices exhibit increased yield and electrostatic stability compared to etched devices, and evidence of ballistic superconductivity is observed. In addition to aluminum, hybrid structures based on tantalum, niobium, and vanadium are presented.

Flux-induced topological superconductivity in full-shell nanowires

Hybrid semiconductor-superconductor nanowires have emerged as a promising platform for realizing topological superconductivity (TSC). Here, we present a route to TSC using magnetic flux applied to a full superconducting shell surrounding a semiconducting nanowire core. 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 zero-energy state around one applied flux quantum, corresponding to 2π phase winding. Theoretical analysis indicates that the winding of the superconducting phase can induce a transition to a topological phase supporting Majorana zero modes. Measured Coulomb blockade peak spacing around one flux quantum shows a length dependence that is consistent with the existence of Majorana modes at the ends of the nanowire.