Scaling Theory of Conduction Through a Normal-Superconductor Microbridge

TL;DR

This paper develops a scaling theory for the resistance of a disordered normal-metal wire connected to a superconductor, revealing how resistance varies with length and interface transmittance.

Contribution

It provides an exact scaling of transmission eigenvalue distribution with length in the metallic limit using a novel fluid dynamics analogy.

Findings

Resistance has a minimum near length l/Gamma.

Scaling of transmission eigenvalues is obtained exactly.

Resistance behavior depends on wire length and interface transmittance.

Abstract

The length dependence is computed of the resistance of a disordered normal-metal wire attached to a superconductor. The scaling of the transmission eigenvalue distribution with length is obtained exactly in the metallic limit, by a transformation onto the isobaric flow of a two-dimensional ideal fluid. The resistance has a minimum for lengths near l/Gamma, with l the mean free path and Gamma the transmittance of the superconductor interface.