Local Density of States in a Dirty Normal Metal connected to a Superconductor

TL;DR

This paper investigates how a superconductor influences the local density of states in a nearby normal metal, revealing a persistent suppression at low energies and a minigap formation, with magnetic fields diminishing these effects.

Contribution

It provides a detailed analysis of the local density of states in superconductor-normal metal heterostructures, including the effects of layer thickness and magnetic fields, aligning with recent experimental observations.

Findings

Suppression of density of states at small energies persists over large distances.

A minigap appears in thin normal metal layers, proportional to the Thouless energy.

Magnetic fields suppress the proximity-induced features.

Abstract

A superconductor in contact with a normal metal not only induces superconducting correlations, known as proximity effect, but also modifies the density of states at some distance from the interface. These modifications can be resolved experimentally in microstructured systems. We, therefore, study the local density of states $N(E,x)$ of a superconductor - normal metal heterostructure. We find a suppression of $N(E,x)$ at small energies, which persists to large distances. If the normal metal forms a thin layer of thickness $L_n$, a minigap in the density of states appears which is of the order of the Thouless energy $\sim \hbar D/L_n^2$. A magnetic field suppresses the features. We find good agreement with recent experiments of Gu\'eron {\it et al.}