Proximity effect and Majorana bound states in clean semiconductor nanowires coupled to disordered superconductors

TL;DR

This paper investigates how disorder in superconductors affects Majorana bound states in semiconductor nanowires, revealing that strong proximity coupling can suppress the topological gap and alter Majorana localization.

Contribution

It demonstrates nonperturbatively that strong proximity coupling makes the induced superconductivity susceptible to superconductor disorder, impacting Majorana states in nanowires.

Findings

Disorder suppresses the induced gap at zero magnetic field under strong coupling.

Strong coupling reduces Majorana localization length, affecting topological gap stability.

Disorder can eliminate the topological gap even in short wires.

Abstract

We study a semiconductor wire with strong spin-orbit coupling, which is proximity-coupled to a superconductor with chemical potential disorder. When tunneling at the semiconductor- superconductor interface is very weak, it is known that disorder in the superconductor does not affect the induced superconductivity nor, therefore, the effective topological superconductivity that emerges above a critical magnetic field. We demonstrate nonperturbatively how this result breaks down with stronger proximity coupling by obtaining the low-energy (i.e., subgap) excitation spectrum through direct numerical diagonalization of an appropriate BdG hamiltonian. With strong proximity coupling, we find that disorder in the parent superconductor suppresses the (non- topological) induced gap at zero magnetic field by disordering the induced pair potential. In the topological superconducting phase at large magnetic field, strong proximity coupling reduces the localization length of Majorana bound states, such that the induced disorder eliminates the topological gap while bulk Majorana zero modes emerge, even for short wires.