Random Scattering Matrices and the Circuit Theory of Andreev Conductances

TL;DR

This paper develops a method to calculate conductance in mesoscopic normal-metal systems near superconductors, extending Nazarov's circuit theory by averaging scattering matrices over the circular orthogonal ensemble.

Contribution

It introduces a novel approach combining scattering matrix averaging with circuit theory, bridging scattering and bulk methods for conductance calculations.

Findings

Reproduces Nazarov's circuit theory results

Extends the theory to heat conductance

Provides a unified framework for electrical and thermal conductance

Abstract

The conductance of a normal-metal mesoscopic system in proximity to superconducting electrode(s) is calculated. The normal-metal part may have a general geometry, and is described as a ``circuit'' with ``leads'' and ``junctions''. The junctions are each ascribed a scattering matrix which is averaged over the circular orthogonal ensemble, using recently-developed techniques. The results for the electrical conductance reproduce and extend Nazarov's circuit theory, thus bridging between the scattering and the bulk approaches. The method is also applied to the heat conductance.