Proximity-induced superconductivity generated by thin films: Effects of Fermi surface mismatch and disorder in the superconductor

TL;DR

This study explores how disorder and Fermi surface mismatch in thin superconducting films influence proximity-induced superconductivity, revealing complex effects on superconducting strength and topological phases.

Contribution

It provides a detailed numerical analysis of disorder effects on proximity-induced superconductivity in thin films, highlighting the interplay between Fermi surface mismatch, disorder, and topological phases.

Findings

Proximity effect is significantly reduced in thin films compared to bulk superconductors.

Disorder can enhance proximity-induced superconductivity but also introduces effective disorder in the semiconductor.

Thickness-dependent variations in superconductivity are suppressed by disorder.

Abstract

We investigate the effects of disorder characterising a superconducting thin film on the proximity-induced superconductivity generated by the film (in, e.g., a semiconductor) based on the exact numerical analysis of a three-dimensional microscopic model. To make the problem numerically tractable, we use a recursive Green's function method in combination with a patching approach that exploits the short-range nature of the interface Green's function in the presence of disorder. As a result of the Fermi surface mismatch between the superconductor (SC) and the semiconductor (SM) in combination with the confinement-induced quantization of the transverse SC modes, the proximity effect induced by a clean SC film is typically one to three orders of magnitude smaller that the corresponding quantity for a bulk SC and exhibits huge thickness-dependent variations. The presence of disorder has competing effects: on the one hand it enhances the proximity-induced superconductivity and suppresses its strong thickness dependence, on the other hand it generates proximity-induced effective disorder in the SM. The effect of proximity-induced disorder on the topological superconducting phase and the associated Majorana modes is studied nonperturbatively.