Spectral Features of the Proximity Effect

TL;DR

This paper investigates how the local density of states in superconductor-normal metal sandwiches varies with impurity concentration, revealing different gap behaviors in clean and dirty regimes.

Contribution

It provides a comprehensive calculation of the LDOS at arbitrary impurity levels, bridging the gap between ballistic and diffusive limits.

Findings

Superconductor induces a gap proportional to inverse mean free path in clean systems.

In dirty systems, the gap scales with the mean free path, matching Usadel equation predictions.

The study unifies understanding of proximity effects across impurity regimes.

Abstract

We calculate the local density of states (LDOS) of a superconductor-normal metal sandwich at arbitrary impurity concentration. The presence of the superconductor induces a gap in the normal metal spectrum that is proportional to the inverse of the elastic mean free path $l$ for rather clean systems. For a mean free path much shorter than the thickness of the normal metal, we find a gap size proportional to $l$ that approaches the behavior predicted by the Usadel equation (diffusive limit).