Distinguishing trivial and topological zero-energy states in long nanowire junctions

Jorge Cayao,Annica M Black-Schaffer

doi:10.1103/physrevb.104.l020501

Abstract

The emergence of zero energy states in non-topological superconductors represents an inevitable problem that obscures the proper identification of zero energy Majorana bound states (MBSs) and prevents their use as topologically protected qubits. In this Research Letter we investigate long superconductor-normal-superconductor junctions where trivial zero energy states, robust over a large range of parameters, appear as a result of helicity and confinement in the normal region. We demonstrate that both equilibrium supercurrents and critical currents are sensitive to variations in the length of the superconductor regions in the topological phase hosting MBSs, but, remarkably, no such length dependence exists when robust, but trivial, zero energy states are present. This strikingly different response originates from the non-local nature of the MBSs and we, therefore, propose it as a simple protocol for distinguishing between trivial and topological zero energy states.

Highlights

The realization of topological superconductivity and Majorana bound states (MBSs) has generated a great deal of attention in physics, because MBSs represent a new superconducting state and due to their potential for applications [1,2,3,4,5,6]
This helical regime is found at low magnetic fields and occurs as an inevitable interim phase before the topological phase at higher fields, which further complicates detecting MBSs
zero-energy states (ZESs) in the helical regime and topological MBSs are still elusive. In this Research Letter we show how equilibrium phasebiased transport in long SNS junctions based on nanowires with spin-orbit coupling (SOC) [see Fig. 1(a)] can clearly distinguish between robust trivial ZESs and topological MBSs

Summary

Introduction

The realization of topological superconductivity and Majorana bound states (MBSs) has generated a great deal of attention in physics, because MBSs represent a new superconducting state and due to their potential for applications [1,2,3,4,5,6]. In this Research Letter we show how equilibrium phasebiased transport in long SNS junctions based on nanowires with SOC [see Fig. 1(a)] can clearly distinguish between robust trivial ZESs and topological MBSs. In particular, we design a test of nonlocality, unique to MBSs, using supercurrents and critical currents by varying the lengths of the superconducting S regions.

Results

Conclusion