Nonlinearity in NS transport: scattering matrix approach

TL;DR

This paper derives a comprehensive formula for current in disordered normal-superconducting junctions, accounting for finite temperature, voltage dependence, and scattering processes, advancing understanding of transport phenomena in such systems.

Contribution

It introduces a general scattering matrix approach to describe current in NS junctions, including effects of Andreev scattering and finite temperature, extending previous models.

Findings

Derived a formula for current involving multichannel scattering matrices.

Applied the spectral conductance formula to NINIS double barrier junctions.

Discussed symmetry properties of current under voltage reversal.

Abstract

A general formula for the current through a disordered normal--superconducting junction is derived, which is valid at finite temperature and includes the full voltage dependence. The result depends on a multichannel scattering matrix, which describes elastic scattering in the normal region, and accounts for the Andreev scattering at the NS interface. The symmetry of the current with respect to sign reversal in the subgap regime is discussed. The Andreev approximation is used to derive a spectral conductance formula, which applies to voltages both below and above the gap. In a case study the spectral conductance formula is applied to the problem of an NINIS double barrier junction.