Hybrid Superconductor-semiconductor Nanowire Research Articles

Closing of the induced gap in a hybrid superconductor-semiconductor nanowire

Hybrid superconductor-semiconductor nanowires are predicted to undergo a field-induced phase transition from a trivial to a topological superconductor, marked by the closure and re-opening of the excitation gap, followed by the emergence of Majorana bound states at the nanowire ends. Many local density-of-states measurements have reported signatures of the topological phase, however this interpretation has been challenged by alternative explanations. Here, by measuring nonlocal conductance, we identify the closure of the excitation gap in the bulk of the semiconductor before the emergence of zero-bias peaks. This observation is inconsistent with scenarios where zero-bias peaks occur due to end-states with a trivially gapped bulk, which have been extensively considered in the theoretical and experimental literature. We observe that after the gap closes, nonlocal signals fluctuate strongly and persist irrespective of the presence of local-conductance zero-bias peaks. Thus, our observations are also incompatible with a simple picture of clean topological superconductivity. This work presents a new experimental approach for probing the spatial extent of states in Majorana wires, and reveals the presence of a regime with a continuum of spatially extended states and uncorrelated zero-bias peaks.

Distinguishing Majorana and quasi-Majorana bound states in a hybrid superconductor-semiconductor nanowire with inhomogeneous potential barriers

A semiconductor-superconductor hybrid nanowire with a spatially inhomogeneous potential can host partially separated quasi-Majorana bound states (quasi-MBSs). In this work, we consider a two-lead (three-terminal) setup of transport with two different potential barriers and find that for a Majorana nanowire with smooth potential barriers at both ends, the quasi-MBSs can be well-separated at the nanowire’s endpoints just like true MBSs, and the nonlocal conductance process displays parity-related interference behavior in both the quasi-MBS regime and topological regime. By contrast, for a Majorana nanowire with a smooth potential barrier only at one end, the quasi-MBSs are partially separated, and no parity-related interference pattern occurs in the quasi-MBS regime. Our findings provide a simple way to distinguish MBSs from quasi-MBSs and give some insight into quasi-MBS-based quantum computation.

From Andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires

Inhomogeneous superconductors can host electronic excitations, known as Andreev bound states (ABSs), below the superconducting energy gap. With the advent of topological superconductivity, a new kind of zero-energy ABS with exotic qualities, known as a Majorana bound state (MBS), has been discovered. A special property of MBS wavefunctions is their non-locality, which, together with non-Abelian braiding, is the key to their promise in topological quantum computation. We focus on hybrid superconductor–semiconductor nanowires as a flexible and promising experimental platform to realize one-dimensional topological superconductivity and MBSs. We review the main properties of ABSs and MBSs, state-of-the-art techniques for their detection and theoretical progress beyond minimal models, including different types of robust zero modes that may emerge without a band-topological transition.

Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states.

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.

RETRACTED ARTICLE: Epitaxy of advanced nanowire quantum devices

Semiconductor nanowires are ideal for realizing various low-dimensional quantum devices. In particular, topological phases of matter hosting non-Abelian quasiparticles (such as anyons) can emerge when a semiconductor nanowire with strong spin-orbit coupling is brought into contact with a superconductor. To exploit the potential of non-Abelian anyons-which are key elements of topological quantum computing-fully, they need to be exchanged in a well-controlled braiding operation. Essential hardware for braiding is a network of crystalline nanowires coupled to superconducting islands. Here we demonstrate a technique for generic bottom-up synthesis of complex quantum devices with a special focus on nanowire networks with a predefined number of superconducting islands. Structural analysis confirms the high crystalline quality of the nanowire junctions, as well as an epitaxial superconductor-semiconductor interface. Quantum transport measurements of nanowire 'hashtags' reveal Aharonov-Bohm and weak-antilocalization effects, indicating a phase-coherent system with strong spin-orbit coupling. In addition, a proximity-induced hard superconducting gap (with vanishing sub-gap conductance) is demonstrated in these hybrid superconductor-semiconductor nanowires, highlighting the successful materials development necessary for a first braiding experiment. Our approach opens up new avenues for the realization of epitaxial three-dimensional quantum architectures which have the potential to become key components of various quantum devices.

Proximity-induced low-energy renormalization in hybrid semiconductor-superconductor Majorana structures

A minimal model for the hybrid superconductor-semiconductor nanowire Majorana platform is developed that fully captures the effects of the low-energy renormalization of the nanowire modes arising from the presence of the parent superconductor. In this model, the parent superconductor is an active component that participates explicitly in the low-energy physics, not just a passive partner that only provides proximity-induced Cooper pairs for the nanowire. This treatment on an equal footing of the superconductor and the semiconductor has become necessary in view of recent experiments, which do not allow a consistent interpretation based just on the bare semiconductor properties. The general theory involves the evaluation of the exact semiconductor Green function that includes a dynamical self-energy correction arising from the tunnel-coupled superconductor. General conditions for the emergence of topological superconductivity are worked out for single-band as well as multi-band nanowires and detailed numerical results are given for both infinite and finite wire cases. The topological quantum phase diagrams are provided numerically and the Majorana bound states are obtained along with their oscillatory energy splitting behaviors due to wavefunction overlap in finite wires. Renormalization effects are shown to be both qualitatively and quantitatively important in modifying the low-energy spectrum of the nanowire. The results of the theory are found to be in good qualitative agreement with Majorana nanowire experiments, leading to the conclusion that the proximity-induced low-energy renormalization of the nanowire modes by the parent superconductor is of fundamental importance in superconductor-semiconductor hybrid structures. Implications of the general theory for obtaining true zero energy topological Majorana modes are pointed out.

Formation and electronic properties of InSb nanocrosses

Signatures of Majorana fermions have recently been reported from measurements on hybrid superconductor-semiconductor nanowire devices. Majorana fermions are predicted to obey special quantum statistics, known as non-Abelian statistics. To probe this requires an exchange operation, in which two Majorana fermions are moved around one another, which requires at least a simple network of nanowires. Here, we report on the synthesis and electrical characterization of crosses of InSb nanowires. The InSb wires grow horizontally on flexible vertical stems, allowing nearby wires to meet and merge. In this way, near-planar single-crystalline nanocrosses are created, which can be measured by four electrical contacts. Our transport measurements show that the favourable properties of the InSb nanowire devices-high carrier mobility and the ability to induce superconductivity--are preserved in the cross devices. Our nanocrosses thus represent a promising system for the exchange of Majorana fermions.