Low-temperature proximity effect in clean metals

TL;DR

This paper derives an asymptotic solution for the proximity effect at low temperatures in clean metals with electron interactions, revealing a power-law decay of the order parameter influenced by repulsive interactions.

Contribution

It provides a novel low-temperature asymptotic analysis of the Gor'kov equations for clean metals with electron repulsion, extending understanding beyond previous high-temperature models.

Findings

Order parameter decays as 1/x from the boundary

Proximity length depends strongly on electron repulsion

Power-law decay contrasts with exponential decay in traditional models

Abstract

Theories of proximity effect in layered superconductor-normal metal structures usually deal with a hypothetic normal metal with no interaction between electrons and with finite temperatures often close to the superconductor critical temperature. We present an asymptotic solution of the Gor'kov equations in the opposite low-temperature limit for a clean normal metal with a repulsive interaction between electrons. The order parameter in the metal exhibits a power-law decay, Delta(x) is proportional to 1/x, as a function of the distance from the SN boundary, x, with a proximity length strongly depending on the repulsive interaction.