Ballistic superconductivity and tunable π-junctions in InSb quantum wells

Anomalous h/2e Periodicity and Majorana Zero Modes in Chiral Josephson Junctions

Recent experiments reported that quantum Hall chiral edge state-mediated Josephson junctions (chiral Josephson junctions) could exhibit Fraunhofer oscillations with a periodicity of either h/e [Vignaud et al., Nature (London) 624, 545 (2023)NATUAS0028-083610.1038/s41586-023-06764-4] or h/2e [Amet et al., Science 352, 966 (2016)SCIEAS0036-807510.1126/science.aad6203]. While the h/e-periodic component of the supercurrent had been anticipated theoretically before, the emergence of the h/2e periodicity is still not fully understood. In this Letter, we systematically study the Fraunhofer oscillations of chiral Josephson junctions. In chiral Josephson junctions, the chiral edge states coupled to the superconductors become chiral Andreev edge states. We find that in short junctions, the coupling of the chiral Andreev edge states can trigger the h/2e-magnetic flux periodicity. Our theory resolves the important puzzle concerning the appearance of the h/2e periodicity in chiral Josephson junctions. Furthermore, we explain that when the chiral Andreev edge states couple, a pair of localized Majorana zero modes appear at the ends of the Josephson junction, which are robust and independent of the phase difference between the two superconductors. As the h/2e periodicity and the Majorana zero modes have the same physical origin in the wide junction limit, the Fraunhofer oscillation period could be useful in identifying the regime with Majorana zero modes.

Quantum transport in InSb quantum well devices: progress and perspective

InSb, a narrow-band III-V semiconductor, is known for its small bandgap, small electron effective mass, high electron mobility, large effectiveg-factor, and strong spin-orbit interactions. These unique properties make InSb interesting for both industrial applications and quantum information processing. In this paper, we provide a review of recent progress in quantum transport research on InSb quantum well devices. With advancements in the growth of high-quality heterostructures and micro/nano fabrication, quantum transport experiments have been conducted on low-dimensional systems based on InSb quantum wells. Furthermore, ambipolar operations have been achieved in undoped InSb quantum wells, allowing for a systematic study of the band structure and quantum properties of p-type narrow-band semiconductors. Additionally, we introduce the latest research on InAsSb quantum wells as a continuation of exploring physics in semiconductors with even narrower bandgaps.

Selective-Area-Grown PbTe-Pb Planar Josephson Junctions for Quantum Devices

Planar Josephson junctions are predicted to host Majorana zero modes. The material platforms in previous studies are two-dimensional electron gases (InAs, InSb, InAsSb, and HgTe) coupled to a superconductor such as Al or Nb. Here, we introduce a new material platform for planar JJs, the PbTe-Pb hybrid. The semiconductor, PbTe, was grown as a thin film via selective area epitaxy. The Josephson junction was defined by a shadow wall during the deposition of superconductor Pb. Scanning transmission electron microscopy reveals a sharp semiconductor-superconductor interface. Gate-tunable supercurrents and multiple Andreev reflections are observed. A perpendicular magnetic field causes interference patterns of the switching current, exhibiting Fraunhofer-like and SQUID-like behaviors. We further demonstrate a prototype device for Majorana detection wherein phase bias and tunneling spectroscopy are applicable.

Sign reversal of the Josephson inductance magnetochiral anisotropy and 0-π-like transitions in supercurrent diodes

The recent discovery of the intrinsic supercurrent diode effect, and its prompt observation in a rich variety of systems, has shown that non-reciprocal supercurrents naturally emerge when both space-inversion and time-inversion symmetries are broken. In Josephson junctions, non-reciprocal supercurrent can be conveniently described in terms of spin-split Andreev states. Here we demonstrate a sign reversal of the Josephson inductance magnetochiral anisotropy, a manifestation of the supercurrent diode effect. The asymmetry of the Josephson inductance as a function of the supercurrent allows us to probe the current-phase relation near equilibrium, and to probe jumps in the junction ground state. Using a minimal theoretical model, we can then link the sign reversal of the inductance magnetochiral anisotropy to the so-called 0-π-like transition, a predicted but still elusive feature of multichannel junctions. Our results demonstrate the potential of inductance measurements as sensitive probes of the fundamental properties of unconventional Josephson junctions.

Gate-Defined Topological Josephson Junctions in Bernal Bilayer Graphene

Recent experiments on Bernal bilayer graphene (BLG) deposited on monolayer WSe_{2} revealed robust, ultraclean superconductivity coexisting with sizable induced spin-orbit coupling. Here, we propose BLG/WSe_{2} as a platform to engineer gate-defined planar topological Josephson junctions, where the normal and superconducting regions descend from a common material. More precisely, we show that if superconductivity in BLG/WSe_{2} is gapped and emerges from a parent state with intervalley coherence, then Majorana zero-energy modes can form in the barrier region upon applying weak in-plane magnetic fields. Our results spotlight a potential pathway for "internally engineered" topological superconductivity that minimizes detrimental disorder and orbital-magnetic-field effects.

Exceptional degeneracies in non-Hermitian Rashba semiconductors

Exceptional points (EPs) are spectral degeneracies of non-Hermitian (NH) systems where eigenvalues and eigenvectors coalesce, inducing unique topological phases that have no counterpart in the Hermitian realm. Here we consider an NH system by coupling a two-dimensional semiconductor with Rashba spin-orbit coupling (SOC) to a ferromagnet lead and show the emergence of highly tunable EPs along rings in momentum space. Interestingly, these exceptional degeneracies are the endpoints of lines formed by the eigenvalue coalescence at finite real energy, resembling the bulk Fermi arcs commonly defined at zero real energy. We then show that an in-plane Zeeman field provides a way to control these exceptional degeneracies although higher values of non-Hermiticity are required in contrast to the zero Zeeman field regime. Furthermore, we find that the spin projections also coalescence at the exceptional degeneracies and can acquire larger values than in the Hermitian regime. Finally, we demonstrate that the exceptional degeneracies induce large spectral weights, which can be used as a signature for their detection. Our results thus reveal the potential of systems with Rashba SOC for realizing NH bulk phenomena.

Control of Andreev Bound States Using Superconducting Phase Texture

Andreev bound states with opposite phase-inversion asymmetries are observed in local tunneling spectra at the two ends of a superconductor-semiconductor-superconductor planar Josephson junction in the presence of a perpendicular magnetic field, while the nonlocal spectra remain phase symmetric. Spectral signatures agree with a theoretical model, yielding a physical picture in which phase textures in superconducting leads localize and control the position of Andreev bound states in the junction, demonstrating a simple means of controlling the position and size of Andreev states within a planar junction.

Josephson Diode Effect in High-Mobility InSb Nanoflags

We report nonreciprocal dissipation-less transport in single ballistic InSb nanoflag Josephson junctions. Applying an in-plane magnetic field, we observe an inequality in supercurrent for the two opposite current propagation directions. Thus, these devices can work as Josephson diodes, with dissipation-less current flowing in only one direction. For small fields, the supercurrent asymmetry increases linearly with external field, and then it saturates as the Zeeman energy becomes relevant, before it finally decreases to zero at higher fields. The effect is maximum when the in-plane field is perpendicular to the current vector, which identifies Rashba spin-orbit coupling as the main symmetry-breaking mechanism. While a variation in carrier concentration in these high-quality InSb nanoflags does not significantly influence the supercurrent asymmetry, it is instead strongly suppressed by an increase in temperature. Our experimental findings are consistent with a model for ballistic short junctions and show that the diode effect is intrinsic to this material.

Fabrication and characterization of InSb nanosheet/hBN/graphite heterostructure devices

Semiconductor InSb nanosheet/hexagonal boron nitride (hBN)/graphite trilayers are fabricated, and single- and double-gate devices made from the trilayers are realized and characterized. The InSb nanosheets employed in the trilayer devices are epitaxially grown, free-standing, zincblende crystals and are in micrometer lateral sizes. The hBN and graphite flakes are obtained by exfoliation. Each trilayer is made by successively stacking an InSb nanosheet on an hBN flake and on a graphite flake using a home-made alignment stacking/transfer setup. The fabricated single- and double-gate devices are characterized by electrical and/or magnetotransport measurements. In all these devices, the graphite and hBN flakes are employed as the bottom gates and the gate dielectrics. The measurements of a fabricated single bottom-gate field-effect device show that the InSb nanosheet in the device has an electron field-effect mobility of ∼7300 cm²V^-1s^-1and a low gate hysteresis of ∼0.05 V at 1.9 K. The measurements of a double-gate Hall-bar device show that both the top and the bottom gate exhibit strong capacitive couplings to the InSb nanosheet channel and can thus tune the nanosheet channel conduction effectively. The electron Hall mobility in the InSb nanosheet of the Hall-bar device is extracted to be larger than 1.1 × 10⁴cm²V^-1s^-1at a sheet electron density of ∼6.1 × 10¹¹cm^-2and 1.9 K and, thus, the device exhibits well-defined Shubnikov-de Haas oscillations.

Understanding the Morphological Evolution of InSb Nanoflags Synthesized in Regular Arrays by Chemical Beam Epitaxy

InSb nanoflags are grown by chemical beam epitaxy in regular arrays on top of Au-catalyzed InP nanowires synthesized on patterned SiO₂/InP(111)B substrates. Two-dimensional geometry of the nanoflags is achieved by stopping the substrate rotation in the step of the InSb growth. Evolution of the nanoflag length, thickness and width with the growth time is studied for different pitches (distances in one of the two directions of the substrate plane). A model is presented which explains the observed non-linear time dependence of the nanoflag length, saturation of their thickness and gradual increase in the width by the shadowing effect for re-emitted Sb flux. These results might be useful for morphological control of InSb and other III-V nanoflags grown in regular arrays.

InSbAs Two-Dimensional Electron Gases as a Platform for Topological Superconductivity

Topological superconductivity can be engineered in semiconductors with strong spin-orbit interaction coupled to a superconductor. Experimental advances in this field have often been triggered by the development of new hybrid material systems. Among these, two-dimensional electron gases (2DEGs) are of particular interest due to their inherent design flexibility and scalability. Here, we discuss results on a 2D platform based on a ternary 2DEG (InSbAs) coupled to in situ grown aluminum. The spin-orbit coupling in these 2DEGs can be tuned with the As concentration, reaching values up to 400 meV Å, thus exceeding typical values measured in its binary constituents. In addition to a large Landé g-factor of ∼55 (comparable to that of InSb), we show that the clean superconductor-semiconductor interface leads to a hard induced superconducting gap. Using this new platform, we demonstrate the basic operation of phase-controllable Josephson junctions, superconducting islands, and quasi-1D systems, prototypical device geometries used to study Majorana zero modes.

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.

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 ¯].