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Hybrid superconductor–semiconductor nanowires with Rashba spin–orbit coupling are arguably becoming the leading platform for the search of Majorana bound states (MBSs) in engineered topological superconductors. We perform a systematic numerical study of the low-energy Andreev spectrum and supercurrents in short and long superconductor–normal–superconductor junctions made of nanowires with strong Rashba spin–orbit coupling, where an external Zeeman field is applied perpendicular to the spin–orbit axis. In particular, we investigate the detailed evolution of the Andreev bound states from the trivial into the topological phase and their relation with the emergence of MBSs. Due to the finite length, the system hosts four MBSs, two at the inner part of the junction and two at the outer one. They hybridize and give rise to a finite energy splitting at a superconducting phase difference of π, a well-visible effect that can be traced back to the evolution of the energy spectrum with the Zeeman field: from the trivial phase with Andreev bound states into the topological phase with MBSs. Similarly, we carry out a detailed study of supercurrents for short and long junctions from the trivial to the topological phases. The supercurrent, calculated from the Andreev spectrum, is 2π-periodic in the trivial and topological phases. In the latter it exhibits a clear sawtooth profile at a phase difference of π when the energy splitting is negligible, signalling a strong dependence of current–phase curves on the length of the superconducting regions. Effects of temperature, scalar disorder and reduction of normal transmission on supercurrents are also discussed. Further, we identify the individual contribution of MBSs. In short junctions the MBSs determine the current–phase curves, while in long junctions the spectrum above the gap (quasi-continuum) introduces an important contribution.

We study the complete tunneling spectroscopy of a normal metal/p-wave superconductor junction (\\({\\rm N}-p{\\rm S}\\)) and a normal metal/heterostructure superconductor junction (\\({\\rm N}-{\\rm hS}\\)), using the Blonder–Tinkham–Klapwijk (BTK) method. We find that, for a p-wave superconductor with non-trivial topology, there exists a stable quantized zero-bias conductance peak, and for heterostructure superconductors with non-trivial topology, the emerging zero-bias conductance peak is non-quantized and usually has a considerable gap to the quantized value. Furthermore, the latter is sensitive to parameters, especially to spin–orbit coupling and the s-wave pairing potential. All results of the \\({\\rm N}-{\\rm hS}\\) junction we obtained suggest that the observation of a small zero-bias conductance peak, instead of a quantized zero-bias conductance peak, in current tunneling experiments is a natural result. Based on the experiments’ parameters, we find that only by varying the strength of the spin–orbit coupling to be several times smaller than the reported one, can the zero–bias conductance peak be as small as the reported one. Furthermore, the results we obtained suggest that both a stronger spin–orbit coupling and proximity s-wave superconductor with a relatively weaker pairing potential can produce a much more striking zero-bias conductance peak (compared to the experiments), even an almost quantized one. As s-wave superconductors are common in nature, this prediction can be verified using current experiments.

We study the complete tunneling spectroscopy of a normal metal/p-wave superconductor junction ( ) and a normal metal/heterostructure superconductor junction ( ), using the Blonder-Tinkham-Klapwijk (BTK) method. We find that, for a p-wave superconductor with non-trivial topology, there exists a stable quantized zero-bias conductance peak, and for heterostructure superconductors with non-trivial topology, the emerging zero-bias conductance peak is non-quantized and usually has a considerable gap to the quantized value. Furthermore, the latter is sensitive to parameters, especially to spin-orbit coupling and the s-wave pairing potential. All results of the junction we obtained suggest that the observation of a small zero-bias conductance peak, instead of a quantized zero-bias conductance peak, in current tunneling experiments is a natural result. Based on the experiments' parameters, we find that only by varying the strength of the spin-orbit coupling to be several times smaller than the reported one, can the zero-bias conductance peak be as small as the reported one. Furthermore, the results we obtained suggest that both a stronger spin-orbit coupling and proximity s-wave superconductor with a relatively weaker pairing potential can produce a much more striking zero-bias conductance peak (compared to the experiments), even an almost quantized one. As s-wave superconductors are common in nature, this prediction can be verified using current experiments.

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. Advanced fabrication techniques enable a wide range of quantum devices, such as the realization of a topological qubit. Here, the authors introduce an on-chip fabrication technique based on shadow walls to implement topological qubits in an InSb nanowire without fabrication steps such as lithography and etching.

Two-dimensional atomic crystals (2DACs) can be mechanically assembled with precision for the fabrication of heterostructures, allowing for the combination of material building blocks with great flexibility. In addition, while conventional nanolithography can be detrimental to most of the 2DACs which are not sufficiently inert, mechanical assembly potentially minimizes the nanofabrication processing and preserves the intrinsic physical properties of the 2DACs. In this work we study the interfacial charge transport between various 2DACs and electrical contacts, by fabricating and characterizing 2DAC-superconductor junctions through mechanical transfer. Compared to devices fabricated with conventional nanolithography, mechanically assembled devices show comparable or better interface transparency. Surface roughness at the electrical contacts is identified to be a major limitation to the interface quality.

We theoretically show quasiparticles-driven thermal diode effect (TDE) in an inversion symmetry-broken Weyl superconductor (WSC)-Weyl semimetal (WSM)-WSC Josephson junction. A Zeeman field perpendicular to the WSM region of the thermally-biased Weyl Josephson junction (WJJ) induces an asymmetry between the forward and reverse thermal currents, which is responsible for the TDE. Most interestingly, we show that the sign and magnitude of the thermal diode rectification coefficient is highly tunable by the superconducting phase difference and external Zeeman field, and also strongly depends on the junction length. The tunability of the rectification, particularly, the sign changing behavior associated with higher rectification enhances the potential of our WJJ thermal diode to use as functional switching components in thermal devices.

For a Josephson junction array with hybrid superconductor/metal/superconductor junctions, a quantum phase transition from a superconducting to a two-dimensional (2D) metallic ground state is predicted to occur on increasing the junction normal state resistance. Owing to its surface-exposed 2D electron gas and its gate-tunable charge carrier density, graphene coupled to superconductors is the ideal platform to study such phase transitions between ground states. Here, we show that decorating graphene with a sparse and regular array of superconducting discs enables the continuous gate-tuning of the quantum superconductor-to-metal transition of the Josephson junction array into a zero-temperature metallic state. The suppression of proximity-induced superconductivity is a direct consequence of the emergence of quantum fluctuations of the superconducting phase of the discs. Under perpendicular magnetic fields, the competition between quantum fluctuations and disorder is responsible for the resilience of superconductivity at the lowest temperatures, supporting a glassy state that persists above the upper critical field. We provide the entire phase diagram of the disorder and magnetic-field-tuned transition to reveal the role of quantum phase fluctuations in 2D superconducting systems. When superconducting discs are deposited on graphene they induce local superconducting islands. The phase coupling between the islands can be controlled by a gate. Quantum phase fluctuations kill the superconductivity and lead to a metallic state, however, at higher magnetic fields superconductivity can return.

A clear demonstration of topological superconductivity (TS) and Majorana zero modes remains one of the major pending goals in the field of topological materials. One common strategy to generate TS is through the coupling of an s -wave superconductor to a helical half-metallic system. Numerous proposals for the latter have been put forward in the literature, most of them based on semiconductors or topological insulators with strong spin-orbit coupling. Here, we demonstrate an alternative approach for the creation of TS in graphene-superconductor junctions without the need for spin-orbit coupling. Our prediction stems from the helicity of graphene’s zero-Landau-level edge states in the presence of interactions and from the possibility, experimentally demonstrated, of tuning their magnetic properties with in-plane magnetic fields. We show how canted antiferromagnetic ordering in the graphene bulk close to neutrality induces TS along the junction and gives rise to isolated, topologically protected Majorana bound states at either end. We also discuss possible strategies to detect their presence in graphene Josephson junctions through Fraunhofer pattern anomalies and Andreev spectroscopy. The latter, in particular, exhibits strong unambiguous signatures of the presence of the Majorana states in the form of universal zero-bias anomalies. Remarkable progress has recently been reported in the fabrication of the proposed type of junctions, which offers a promising outlook for Majorana physics in graphene systems.

Andreev reflection is an important quantum tunneling phenomenon in the conductor-superconductor junction. The Andreev reflection coefficients T AR of a hybrid system with s -wave superconductor connected by topological nodal-line semimetals (TNLSMs-SC junction system) is calculated theoretically by using the Landauer–Büttiker formula combined with the nonequilibrium Green’s function method. The results show that when the direction of the boundary state electron and the incident electron are the same, only the bulk states of the TNLSMs involve the Andreev reflection of the hybrid system, and the Andreev reflection coefficients T AR enhance with the increase of the Fermi energy E F . We also study the effect of on-site energy ε z and mass term m on the Andreev reflection and find that the Andreev reflection in the system decreases rapidly with the increase of on-site energy ε z and mass term m . Moreover, we find that only in the presence of a mass term m , the Andreev reflection coefficients T AR of the system changes with the rise of the Fermi energy E F . When a perpendicular magnetic field is applied in the system, the Andreev reflection coefficients T AR in the superconducting gap will appear a series of oscillating peaks. For a hybrid system with the large perpendicular magnetic field applied, we find that the maximum Andreev reflection coefficients T AR = 7.2 at the Fermi energy E F = 0.0 and the incident electron energy E = ± 0.1 . The Andreev reflection coefficients T AR is gradually enhanced in the superconducting gap (incident energy | E | ⩽ 0.2 ) when a disorder is applied to the superconductor region of the system. However, the symmetry of the Andreev reflection coefficients T AR is broken when the perpendicular magnetic field is applied to the system. These peculiar transport properties of the TNLSMs-SC junction system are expected to provide theoretical guidance for future applications.

We theoretically investigate the Andreev reflection of the massive pseudospin-1 Dirac fermions including the + U -type, the − U -type, and the S z -type mass terms, corresponding to the flat band locating at the top, the bottom, and the center of the band gap, respectively. For the ± U -type fermions, it is found that the Andreev reflection probability at the oblique incidence can be even larger than that at the normal incidence. For the retro-reflection, such an oblique enhancement occurs in the n -doped + U -type ( p -doped − U -type) massive fermion systems. While for the specular reflection, the enhancement occurs in the n -doped − U -type ( p -doped + U -type) systems. For the S z -type massive fermions, an ideal Andreev reflection with all-angle unit efficiency is predicted in an undoped junction with the incident energy equal to the superconducting gap.