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

Jorge Cayao,Ramón Aguado,Elsa Prada,Annica M Black-Schaffer

doi:10.3762/bjnano.9.127

Abstract

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.

Highlights

A semiconducting nanowire with strong Rashba spin–orbit coupling (SOC) with proximity-induced s-wave superconducting correlations can be tuned into a topological superconductor by means of an external Zeeman field [1,2,3]
In section “Nanowire model” we describe the model for semiconducting nanowires with SOC, where we show that only the right combination of Rashba SOC, a Zeeman field perpendicular to the spin–orbit axis and s-wave superconductivity leads to the emergence of Majorana bound states (MBSs)
) SNS junctions based on nanowires with Rashba SOC and in the presence of a Zeeman field

Summary

Introduction

A semiconducting nanowire with strong Rashba spin–orbit coupling (SOC) with proximity-induced s-wave superconducting correlations can be tuned into a topological superconductor by means of an external Zeeman field [1,2,3]. In the case of weak SOC the minigap is reduced and for high Zeeman field it might acquire very small values, affecting the topological protection of the MBSs. To complement this introductory part, calculations of the wavefunctions and charge density associated with the lowest levels of the topological superconducting nanowire spectrum are presented in the Supporting Information File 1.

Results

Conclusion