Hard gap in epitaxial semiconductor-superconductor nanowires

Shadowed versus Etched Superconductor-Semiconductor Junctions in Al/InAs Nanowires

Hybrid semiconductor-superconductor nanowires have emerged as a cornerstone in modern quantum devices. Integrating such nanowires into hybrid devices typically requires extensive postgrowth processing which may affect device performance unfavorably. Here, we present a technique for in situ shadowing superconductors on nanowires and compare the structural and electronic properties of Al junctions formed by shadowing versus etching. Based on transmission electron microscopy, we find that typical etching procedures lead to atomic-scale surface roughening. This surface perturbation may cause a reduction of the electron mobility as demonstrated in transport measurements. Further, we display advanced shadowing geometries aiding in the pursuit of bringing fabrication of hybrid devices in situ. Finally, we give examples of shadowed junctions exploited in various device geometries that exhibit high-quality quantum transport signatures.

Electronic Transport and Quantum Phenomena in Nanowires

Nanowires are natural one-dimensional channels and offer new opportunities for advanced electronic quantum transport experiments. We review recent progress on the synthesis of nanowires and methods for the fabrication of hybrid semiconductor/superconductor systems. We discuss methods to characterize their electronic properties in the context of possible future applications such as topological and spin qubits. We focus on group III-V (InAs and InSb) and group IV (Ge/Si) semiconductors, since these are the most developed, and give an outlook on other potential materials.

Majorana Zero Modes Induced by the Meissner Effect at Small Magnetic Field

One key difficulty in realizing Majorana zero modes (MZMs) is the required high magnetic field, which causes serious issues, e.g., shrinks the superconducting gap, reduces topological region, and weakens their robustness against disorders. In this Letter, we propose that the Meissner effect can bring the topological superconducting phase to a superconductor/topological-insulator/superconductor (SC/TI/SC) hybrid system. Remarkably, the required magnetic field strength (<10  mT) to support MZMs has been reduced by several orders of magnitude compared to that (>0.5  T) in the previous schemes. Tuning the phase difference between the top and bottom superconductors can control the number and position of the MZMs. In addition, we account for the electrostatic potential in the superconductor/topological-insulator (SC/TI) interface through the self-consistent Schrödinger-Poisson calculation, which shows the experimental accessibility of our proposal. Our proposal only needs a small magnetic field of less than 10 mT and is robust against the chemical potential fluctuation, which makes the SC/TI/SC hybrid an ideal Majorana platform.

Ballistic PbTe Nanowire Devices

Disorder is the primary obstacle in the current Majorana nanowire experiments. Reducing disorder or achieving ballistic transport is thus of paramount importance. In clean and ballistic nanowire devices, quantized conductance is expected, with plateau quality serving as a benchmark for disorder assessment. Here, we introduce ballistic PbTe nanowire devices grown by using the selective-area-growth (SAG) technique. Quantized conductance plateaus in units of 2e2/h are observed at zero magnetic field. This observation represents an advancement in diminishing disorder within SAG nanowires as most of the previously studied SAG nanowires (InSb or InAs) have not exhibited zero-field ballistic transport. Notably, the plateau values indicate that the ubiquitous valley degeneracy in PbTe is lifted in nanowire devices. This degeneracy lifting addresses an additional concern in the pursuit of Majorana realization. Moreover, these ballistic PbTe nanowires may enable the search for clean signatures of the spin-orbit helical gap in future devices.

Dynamical Polarization of the Fermion Parity in a Nanowire Josephson Junction

Josephson junctions in InAs nanowires proximitized with an Al shell can host gate-tunable Andreev bound states. Depending on the bound state occupation, the fermion parity of the junction can be even or odd. Coherent control of Andreev bound states has recently been achieved within each parity sector, but it is impeded by incoherent parity switches due to excess quasiparticles in the superconducting environment. Here, we show that we can polarize the fermion parity dynamically using microwave pulses by embedding the junction in a superconducting LC resonator. We demonstrate polarization up to 94%±1% (89%±1%) for the even (odd) parity as verified by single shot parity readout. Finally, we apply this scheme to probe the flux-dependent transition spectrum of the even or odd parity sector selectively, without any postprocessing or heralding.

Demonstration of the Nonlocal Josephson Effect in Andreev Molecules

We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current-phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ0-junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.

Sn/InAs Josephson Junctions on Selective Area Grown Nanowires with in Situ Shadowed Superconductor Evaporation

Superconductor-semiconductor nanowire hybrid structures are useful in fabricating devices for quantum information processing. While selective area growth (SAG) offers the flexibility to grow semiconductor nanowires in arbitrary geometries, in situ evaporation of superconductors ensures pristine superconductor-semiconductor interfaces, resulting in strong induced superconductivity in the semiconducting nanowire. In this work, we used high-aspect-ratio SiOx dielectric walls to in situ evaporate islands of superconductor tin on in-plane InAs SAG nanowires. Our technique enables customization in the designs of such hybrid nanostructures, while simultaneously performing the nanowire and superconductor growth without breaking vacuum. Using this technique, we grew super(S)-normal(N)-super(S), NS, and SNSNS junctions. We performed cryogenic electron transport measurements revealing the presence of gate and field tunable supercurrents. We further measured the superconducting gap and critical fields in the hybrid nanostructures and the crossover from 2e to 1e periodicity in the SNSNS junctions as a proof of the usability of these hybrid nanostructures.

Supercurrent, Multiple Andreev Reflections and Shapiro Steps in InAs Nanosheet Josephson Junctions

We report an experimental study of proximity induced superconductivity in planar Josephson junction devices made from free-standing InAs nanosheets. The nanosheets are grown by molecular beam epitaxy, and the Josephson junction devices are fabricated by directly contacting the nanosheets with superconductor Al electrodes. The fabricated devices are explored by low-temperature carrier transport measurements. The measurements show that the devices exhibit a gate-tunable supercurrent, multiple Andreev reflections, and a good quality superconductor-semiconductor interface. The superconducting characteristics of the Josephson junctions are investigated at different magnetic fields and temperatures and are analyzed based on the Bardeen-Cooper-Schrieffer (BCS) theory. The measurements of the ac Josephson effect are also conducted under microwave radiations with different radiation powers and frequencies, and integer Shapiro steps are observed. Our work demonstrates that InAs nanosheet based hybrid devices are desired systems for investigating the forefront of physics, such as two-dimensional topological superconductivity.

The Schottky barrier transistor in emerging electronic devices

This paper explores how the Schottky barrier (SB) transistor is used in a variety of applications and material systems. A discussion of SB formation, current transport processes, and an overview of modeling are first considered. Three discussions follow, which detail the role of SB transistors in high performance, ubiquitous and cryogenic electronics. For high performance computing, the SB typically needs to be minimized to achieve optimal performance and we explore the methods adopted in carbon nanotube technology and two-dimensional electronics. On the contrary for ubiquitous electronics, the SB can be used advantageously in source-gated transistors and reconfigurable field-effect transistors (FETs) for sensors, neuromorphic hardware and security applications. Similarly, judicious use of an SB can be an asset for applications involving Josephson junction FETs.

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.

Measurements of Phase Dynamics in Planar Josephson Junctions and SQUIDs

We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.

InAs/MoRe Hybrid Semiconductor/Superconductor Nanowire Devices

Implementing superconductors capable of proximity-inducing a large energy gap in semiconductors in the presence of strong magnetic fields is a major goal toward applications of semiconductor/superconductor hybrid materials in future quantum information technologies. Here, we study the performance of devices consisting of InAs nanowires in electrical contact with molybdenum-rhenium (MoRe) superconducting alloys. The MoRe thin films exhibit transition temperatures of ∼10 K and critical fields exceeding 6 T. Normal/superconductor devices enabled tunnel spectroscopy of the corresponding induced superconductivity, which was maintained up to ∼10 K, and MoRe-based Josephson devices exhibited supercurrents and multiple Andreev reflections. We determine an induced superconducting gap lower than expected from the transition temperature and observe gap softening at finite magnetic field. These may be common features for hybrids based on large-gap, type II superconductors. The results encourage further development of MoRe-based hybrids.

Plateau Regions for Zero-Bias Peaks within 5% of the Quantized Conductance Value 2e^{2}/h

Probing an isolated Majorana zero mode is predicted to reveal a tunneling conductance quantized at 2e^{2}/h at zero temperature. Experimentally, a zero-bias peak (ZBP) is expected and its height should remain robust against relevant parameter tuning, forming a quantized plateau. Here, we report the observation of large ZBPs in a thin InAs-Al hybrid nanowire device. The ZBP height can stick close to 2e^{2}/h, mostly within 5% tolerance, by sweeping gate voltages and magnetic field. We further map out the phase diagram and identify two plateau regions in the phase space. Despite the presence of disorder and quantum dots, our result constitutes a step forward toward establishing Majorana zero modes.

Photon-Assisted Tunneling of High-Order Multiple Andreev Reflections in Epitaxial Nanowire Josephson Junctions

Semiconductor/superconductor hybrids exhibit a range of phenomena that can be exploited for the study of novel physics and the development of new technologies. Understanding the origin of the energy spectrum of such hybrids is therefore a crucial goal. Here, we study Josephson junctions defined by shadow epitaxy on InAsSb/Al nanowires. The devices exhibit gate-tunable supercurrents at low temperatures and multiple Andreev reflections (MARs) at finite voltage bias. Under microwave irradiation, photon-assisted tunneling (PAT) of MARs produces characteristic oscillating sidebands at quantized energies, which depend on MAR order, n, in agreement with a recently suggested modification of the classical Tien-Gordon equation. The scaling of the quantized energy spacings with microwave frequency provides independent confirmation of the effective charge, ne, transferred by the nth-order tunneling process. The measurements suggest PAT as a powerful method for assigning the origin of low-energy spectral features in hybrid Josephson devices.

Manifestation of Majorana modes overlap in the Aharonov-Bohm effect

One of the key features of the Majorana bound states emerging in topological superconducting (SC) wires is increasing oscillations of their energy under the growth of magnetic field or chemical potential due to concomitant enhancement of hybridization of the Majorana mode wave functions initially localized at the opposite edges of the structure. In this study we found that the other consequence of it is a shift of Aharonov-Bohm (AB) oscillations of linear-response conductance in an interference device where two ends of the SC wire connected with a normal contact via non-SC wires (arms). In addition, it is accompanied by an oscillation period doubling. The numerical calculations for the spinful system are supported by the analytical results for different spinless models allowing to track the conductance evolution as the hybridization of the Majorana modes increases. It is shown that since the coupling between the different arms and normal contact is implemented only via the different-type Majoranas the AB oscillations acquire a fundamentalπ/2 shift in comparison with the effect for an analogous system of zero-energy quantum dots.

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.

Signatures of Andreev Blockade in a Double Quantum Dot Coupled to a Superconductor

We investigate an electron transport blockade regime in which a spin triplet localized in the path of current is forbidden from entering a spin-singlet superconductor. To stabilize the triplet, a double quantum dot is created electrostatically near a superconducting Al lead in an InAs nanowire. The quantum dot closest to the normal lead exhibits Coulomb diamonds, and the dot closest to the superconducting lead exhibits Andreev bound states and an induced gap. The experimental observations compare favorably to a theoretical model of Andreev blockade, named so because the triplet double dot configuration suppresses Andreev reflections. Observed leakage currents can be accounted for by finite temperature. We observe the predicted quadruple level degeneracy points of high current and a periodic conductance pattern controlled by the occupation of the normal dot. Even-odd transport asymmetry is lifted with increased temperature and magnetic field. This blockade phenomenon can be used to study spin structure of superconductors. It may also find utility in quantum computing devices that use Andreev or Majorana states.

Semiconductor Epitaxy in Superconducting Templates

Integration of high-quality semiconductor-superconductor devices into scalable and complementary metal-oxide-semiconductor compatible architectures remains an outstanding challenge, currently hindering their practical implementation. Here, we demonstrate growth of InAs nanowires monolithically integrated on Si inside lateral cavities containing superconducting TiN elements. This technique allows growth of hybrid devices characterized by sharp semiconductor-superconductor interfaces and with alignment along arbitrary crystallographic directions. Electrical characterization at low temperature reveals proximity induced superconductivity in InAs via a transparent interface.

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.

Friction of magnetene, a non-van der Waals 2D material

Two-dimensional (2D) materials are known to have low-friction interfaces by reducing the energy dissipated by sliding contacts. While this is often attributed to van der Waals (vdW) bonding of 2D materials, nanoscale and quantum confinement effects can also act to modify the atomic interactions of a 2D material, producing unique interfacial properties. Here, we demonstrate the low-friction behavior of magnetene, a non-vdW 2D material obtained via the exfoliation of magnetite, showing statistically similar friction to benchmark vdW 2D materials. We find that this low friction is due to 2D confinement effects of minimized potential energy surface corrugation, lowered valence states reducing surface adsorbates, and forbidden low-damping phonon modes, all of which contribute to producing a low-friction 2D material.

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.

Al-Ge-Al Nanowire Heterostructure: From Single-Hole Quantum Dot to Josephson Effect

Superconductor-semiconductor-superconductor heterostructures are attractive for both fundamental studies of quantum phenomena in low-dimensional hybrid systems as well as for future high-performance low power dissipating nanoelectronic and quantum devices. In this work, ultrascaled monolithic Al-Ge-Al nanowire heterostructures featuring monocrystalline Al leads and abrupt metal-semiconductor interfaces are used to probe the low-temperature transport in intrinsic Ge (i-Ge) quantum dots. In particular, demonstrating the ability to tune the Ge quantum dot device from completely insulating, through a single-hole-filling quantum dot regime, to a supercurrent regime, resembling a Josephson field effect transistor with a maximum critical current of 10 nA at a temperature of 390 mK. The realization of a Josephson field-effect transistor with high junction transparency provides a mechanism to study sub-gap transport mediated by Andreev states. The presented results reveal a promising intrinsic Ge-based architecture for hybrid superconductor-semiconductor devices for the study of Majorana zero modes and key components of quantum computing such as gatemons or gate tunable superconducting quantum interference devices.

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.

Structure prediction of epitaxial inorganic interfaces by lattice and surface matching with Ogre

We present a new version of the Ogre open source Python package with the capability to perform structure prediction of epitaxial inorganic interfaces by lattice and surface matching. In the lattice matching step, a scan over combinations of substrate and film Miller indices is performed to identify the domain-matched interfaces with the lowest mismatch. Subsequently, surface matching is conducted by Bayesian optimization to find the optimal interfacial distance and in-plane registry between the substrate and the film. For the objective function, a geometric score function is proposed based on the overlap and empty space between atomic spheres at the interface. The score function reproduces the results of density functional theory (DFT) at a fraction of the computational cost. The optimized interfaces are pre-ranked using a score function based on the similarity of the atomic environment at the interface to the bulk environment. Final ranking of the top candidate structures is performed with DFT. Ogre streamlines DFT calculations of interface energies and electronic properties by automating the construction of interface models. The application of Ogre is demonstrated for two interfaces of interest for quantum computing and spintronics, Al/InAs and Fe/InSb.

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.

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.

Competing Energy Scales in Topological Superconducting Heterostructures

Artificially engineered topological superconductivity has emerged as a viable route to create Majorana modes. In this context, proximity-induced superconductivity in materials with a sizable spin-orbit coupling has been intensively investigated in recent years. Although there is convincing evidence that superconductivity may indeed be induced, it has been difficult to elucidate its topological nature. Here, we engineer an artificial topological superconductor by progressively introducing superconductivity (Nb), strong spin-orbital coupling (Pt), and topological states (Bi₂Te₃). Through spectroscopic imaging of superconducting vortices within the bare s-wave superconducting Nb and within proximitized Pt and Bi₂Te₃ layers, we detect the emergence of a zero-bias peak that is directly linked to the presence of topological surface states. Our results are rationalized in terms of competing energy trends which are found to impose an upper limit to the size of the minigap separating Majorana and trivial modes, its size being ultimately linked to fundamental materials properties.

Josephson Inductance as a Probe for Highly Ballistic Semiconductor-Superconductor Weak Links

We present simultaneous measurements of Josephson inductance and dc transport characteristics of ballistic Josephson junctions based upon an epitaxial Al-InAs heterostructure. The Josephson inductance at finite current bias directly reveals the current-phase relation. The proximity-induced gap, the critical current and the average value of the transparency τ[over ¯] are extracted without need for phase bias, demonstrating, e.g., a near-unity value of τ[over ¯]=0.94. Our method allows us to probe the devices deeply in the nondissipative regime, where ordinary transport measurements are featureless. In perpendicular magnetic field the junctions show a nearly perfect Fraunhofer pattern of the critical current, which is insensitive to the value of τ[over ¯]. In contrast, the signature of supercurrent interference in the inductance turns out to be extremely sensitive to τ[over ¯].

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.

Parity-Protected Superconductor-Semiconductor Qubit

Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parity-protected qubit based on voltage-controlled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energy-phase relation of few-channel junctions. A symmetric interferometer formed by two such junctions, gate-tuned into balance and frustrated by a half-quantum of applied flux, yields a cos(2φ) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate that relaxation of the qubit can be suppressed tenfold by tuning into the protected regime.

Observation of Vanishing Charge Dispersion of a Nearly Open Superconducting Island

Isolation from the environment determines the extent to which charge is confined on an island, which manifests as Coulomb oscillations, such as charge dispersion. We investigate the charge dispersion of a nanowire transmon hosting a quantum dot in the junction. We observe rapid suppression of the charge dispersion with increasing junction transparency, consistent with the predicted scaling law, which incorporates two branches of the Josephson potential. We find improved qubit coherence times at the point of highest suppression, suggesting novel approaches for building charge-insensitive qubits.

Suppressed Charge Dispersion via Resonant Tunneling in a Single-Channel Transmon

We demonstrate strong suppression of charge dispersion in a semiconductor-based transmon qubit across Josephson resonances associated with a quantum dot in the junction. On resonance, dispersion is drastically reduced compared to conventional transmons with corresponding Josephson and charging energies. We develop a model of qubit dispersion for a single-channel resonance, which is in quantitative agreement with experimental data.

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.

Thermoelectric Effect in a Correlated Quantum Dot Side-Coupled to Majorana Bound States

We theoretically study the thermoelectric effect in a hybrid device composed by a topological semiconducting nanowire hosting Majorana bound states (MBSs) and a quantum dot (QD) connected to the left and right non-magnetic electrodes held at different temperatures. The electron-electron Coulomb interactions in the QD are taken into account by the non-equilibrium Green's function technique. We find that the sign change of the thermopower, which is useful for detecting the MBSs, will occur by changing the QD-MBS hybridization strength, the direct overlap between the MBSs at the opposite ends of the nanowire, and the system temperature. Large value of 100% spin-polarized or pure spin thermopower emerges even in the absence of Zeeman splitting in the QD or magnetic electrodes because the MBSs are coupled to electrons of only one certain spin direction in the QD due to the chiral nature of the Majorana fermions. Moreover, the magnitude of the thermopower will be obviously enhanced by the existence of MBSs.

Coherent Epitaxial Semiconductor-Ferromagnetic Insulator InAs/EuS Interfaces: Band Alignment and Magnetic Structure

Hybrid semiconductor-ferromagnetic insulator heterostructures are interesting due to their tunable electronic transport, self-sustained stray field, and local proximitized magnetic exchange. In this work, we present lattice-matched hybrid epitaxy of semiconductor-ferromagnetic insulator InAs/EuS heterostructures and analyze the atomic-scale structure and their electronic and magnetic characteristics. The Fermi level at the InAs/EuS interface is found to be close to the InAs conduction band and in the band gap of EuS, thus preserving the semiconducting properties. Both neutron and X-ray reflectivity measurements show that the overall ferromagnetic component is mainly localized in the EuS thin film with a suppression of the Eu moment in the EuS layer nearest the InAs and magnetic moments outside the detection limits on the pure InAs side. This work presents a step toward realizing defect-free semiconductor-ferromagnetic insulator epitaxial hybrids for spin-lifted quantum and spintronic applications without external magnetic fields.

Controlled dc Monitoring of a Superconducting Qubit

Creating a transmon qubit using semiconductor-superconductor hybrid materials not only provides electrostatic control of the qubit frequency, it also allows parts of the circuit to be electrically connected and disconnected in situ by operating a semiconductor region of the device as a field-effect transistor. Here, we exploit this feature to compare in the same device characteristics of the qubit, such as frequency and relaxation time, with related transport properties such as critical supercurrent and normal-state resistance. Gradually opening the field-effect transistor to the monitoring circuit allows the influence of weak-to-strong dc monitoring of a "live" qubit to be measured. A model of this influence yields excellent agreement with experiment, demonstrating a relaxation rate mediated by a gate-controlled environmental coupling.

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.

Semiconductor-Ferromagnetic Insulator-Superconductor Nanowires: Stray Field and Exchange Field

Nanowires can serve as flexible substrates for hybrid epitaxial growth on selected facets, allowing for the design of heterostructures with complex material combinations and geometries. In this work we report on hybrid epitaxy of freestanding vapor-liquid-solid grown and in-plane selective area grown semiconductor-ferromagnetic insulator-superconductor (InAs/EuS/Al) nanowire heterostructures. We study the crystal growth and complex epitaxial matching of wurtzite and zinc-blende InAs/rock-salt EuS interfaces as well as rock-salt EuS/face-centered cubic Al interfaces. Because of the magnetic anisotropy originating from the nanowire shape, the magnetic structure of the EuS phase is easily tuned into single magnetic domains. This effect efficiently ejects the stray field lines along the nanowires. With tunnel spectroscopy measurements of the density of states, we show that the material has a hard induced superconducting gap, and magnetic hysteretic evolution which indicates that the magnetic exchange fields are not negligible. These hybrid nanowires fulfill key material requirements for serving as a platform for spin-based quantum applications, such as scalable topological quantum computing.

Hard Superconducting Gap and Diffusion-Induced Superconductors in Ge-Si Nanowires

We show a hard superconducting gap in a Ge-Si nanowire Josephson transistor up to in-plane magnetic fields of 250 mT, an important step toward creating and detecting Majorana zero modes in this system. A hard gap requires a highly homogeneous tunneling heterointerface between the superconducting contacts and the semiconducting nanowire. This is realized by annealing devices at 180 °C during which aluminum interdiffuses and replaces the germanium in a section of the nanowire. Next to Al, we find a superconductor with lower critical temperature (T_C = 0.9 K) and a higher critical field (B_C = 0.9-1.2 T). We can therefore selectively switch either superconductor to the normal state by tuning the temperature and the magnetic field and observe that the additional superconductor induces a proximity supercurrent in the semiconducting part of the nanowire even when the Al is in the normal state. In another device where the diffusion of Al rendered the nanowire completely metallic, a superconductor with a much higher critical temperature (T_C = 2.9 K) and critical field (B_C = 3.4 T) is found. The small size of these diffusion-induced superconductors inside nanowires may be of special interest for applications requiring high magnetic fields in arbitrary direction.

Next steps of quantum transport in Majorana nanowire devices

Majorana zero modes are localized quasiparticles that obey non-Abelian exchange statistics. Braiding Majorana zero modes forms the basis of topologically protected quantum operations which could, in principle, significantly reduce qubit decoherence and gate control errors at the device level. Therefore, searching for Majorana zero modes in various solid state systems is a major topic in condensed matter physics and quantum computer science. Since the first experimental signature observed in hybrid superconductor-semiconductor nanowire devices, this field has witnessed a dramatic expansion in material science, transport experiments and theory. While making the first topological qubit based on these Majorana nanowires is currently an ongoing effort, several related important transport experiments are still being pursued in the near term. These will not only serve as intermediate steps but also show Majorana physics in a more fundamental aspect. In this perspective, we summarize these key Majorana experiments and the potential challenges.

Lattice-Symmetry-Assisted Second-Order Topological Superconductors and Majorana Patterns

We propose a realization of the lattice-symmetry-assisted second-order topological superconductors with corner Majorana zero modes (MZM) based on two-dimensional topological insulators (2DTI). The lattice symmetry can naturally lead to the anisotropic coupling of edge states along different directions to the in-plane magnetic field and conventional s-wave pairings, thus leading to a single MZM located at the corners for various lattice patterns. In particular, we focus on the 2DTI with D_{3d} lattice symmetry and found different types of gap opening for the edge states along the armchair and zigzag edges in a broad range of parameters. As a consequence, a single MZM exists at the corner between the zigzag and armchair edges, and is robust against weakly broken lattice symmetry. We propose to realize such corner MZMs in a variety of polygon patterns, such as triangles and quadrilaterals. We further show their potentials in building the Majorana network through constructing the Majorana Y junction under an in-plane magnetic field.

Dominant nonlocal superconducting proximity effect due to electron-electron interaction in a ballistic double nanowire

Cooper pair splitting (CPS) can induce nonlocal correlation between two normal conductors that are coupled to a superconductor. CPS in a double one-dimensional electron gas is an appropriate platform for extracting a large number of entangled electron pairs and is one of the key ingredients for engineering Majorana fermions with no magnetic field. In this study, we investigated CPS by using a Josephson junction of a gate-tunable ballistic InAs double nanowire. The measured switching current into the two nanowires is significantly larger than the sum of the switching current into the respective nanowires, indicating that interwire superconductivity is dominant compared with intrawire superconductivity. From its dependence on the number of propagating channels in the nanowires, the observed CPS is assigned to one-dimensional electron-electron interaction. Our results will pave the way for the utilization of one-dimensional electron-electron interaction to reveal the physics of high-efficiency CPS and to engineer Majorana fermions in double nanowire systems via CPS.

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.

Superconducting vanadium/indium-arsenide hybrid nanowires

We report MBE synthesis of InAs/vanadium hybrid nanowires. The vanadium was deposited without breaking ultra-high vacuum after InAs nanowire growth, minimizing any effect of oxidation and contamination at the interface between the two materials. We investigated four different substrate temperatures during vanadium deposition, ranging from -150 °C to 250 °C. The structural relation between vanadium and InAs depended on the deposition temperature. The three lower temperature depositions gave vanadium shells with a polycrystalline, granular morphology and the highest temperature resulted in vanadium reacting with the InAs nanowire. We fabricated electronic devices from the hybrid nanowires and obtained a high out-of-plane critical magnetic field, exceeding the bulk value for vanadium. However, size effects arising from the nanoscale grains resulted in the absence of a well-defined critical temperature, as well as device-to-device variation in the resistivity versus temperature dependence during the transition to the superconducting state.

Regaining a Spatial Dimension: Mechanically Transferrable Two-Dimensional InAs Nanofins Grown by Selective Area Epitaxy

We report a method for growing rectangular InAs nanofins with deterministic length, width, and height by dielectric-templated selective-area epitaxy. These freestanding nanofins can be transferred to lay flat on a separate substrate for device fabrication. A key goal was to regain a spatial dimension for device design compared to nanowires, while retaining the benefits of bottom-up epitaxial growth. The transferred nanofins were made into devices featuring multiple contacts for Hall effect and four-terminal resistance studies, as well as a global back-gate and nanoscale local top-gates for density control. Hall studies give a 3D electron density 2.5-5 × 10¹⁷ cm^-3, corresponding to an approximate surface accumulation layer density 3-6 × 10¹² cm^-2 that agrees well with previous studies of InAs nanowires. We obtain Hall mobilities as high as 1200 cm²/(V s), field-effect mobilities as high as 4400 cm²/(V s), and clear quantum interference structure at temperatures as high as 20 K. Our devices show excellent prospects for fabrication into more complicated devices featuring multiple ohmic contacts, local gates, and possibly other functional elements, for example, patterned superconductor contacts, that may make them attractive options for future quantum information applications.

Fano effect in Aharonov-Bohm ring with topologically superconducting bridge

Taking into account an inner structure of the arms of the Aharonov-Bohm ring (AB ring) we have analyzed the transport features related to the topological phase transition which is induced in a superconducting wire (SC wire) with strong spin-orbit interaction (SOI). The SC wire acts as a bridge connecting the arms. The in-plane magnetic-field dependence of linear-response conductance obtained using the nonequilibrium Green's functions in the tight-binding approximation revealed the Breit-Wigner and Fano resonances (FRs) if the wire is in the nontrivial phase. The effect is explained by the presence of two interacting transport channels in the system. As a result, the FRs are attributed to bound states in continuum (BSCs). The BSC lifetime is determined by both hopping parameters between subsystems and the SC-wire properties. It is established that the FR width and position are extremely sensitive to the type of the lowest-energy excitation in the SC wire, the Majorana or Andreev bound state (MBS or ABS, respectively). Moreover, it is shown that in the specific case of the AB ring, the T-shape geometry, the FR disappears for the transport via the MBS and the conductance is equal to one quantum. It doubles in the local transport regime. On the contrary, in the ABS case the local conductance vanishes. The influence of the mean-field Coulomb interactions and diagonal disorder in the SC wire on the FR is investigated.

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.