Random matrix theory of proximity effect in disordered wires

TL;DR

This paper uses random matrix theory to analytically study the local density of states in disordered normal-metal wires near superconductors, extending beyond traditional semiclassical methods and analyzing interface transparency effects.

Contribution

It introduces a scattering-matrix approach to analyze the proximity effect in disordered wires, accounting for wave-function localization and interface transparency.

Findings

Results agree with Usadel equation in the diffusive limit

Extended analysis beyond semiclassical theory

Clarified impact of interface transparency on spectral properties

Abstract

We study analytically the local density of states in a disordered normal-metal wire at ballistic distance to a superconductor. Our calculation is based on a scattering-matrix approach, which concerns for wave-function localisation in the normal metal, and extends beyond the conventional semiclassical theory based on Usadel and Eilenberger equations. We also analyse how a finite transparency of the NS interface modifies the spectral proximity effect and demonstrate that our results agree in the dirty diffusive limit with those obtained from the Usadel equation.