Andreev reflection and the semiclassical Bogoliubov-de Gennes Hamiltonian: resonant states

TL;DR

This paper develops a semi-classical framework to analyze Andreev resonant states in imperfect mesoscopic SNS junctions, extending previous models to include junction imperfections and calculating resonance properties.

Contribution

It introduces a semi-classical approach for resonant Andreev states in non-ideal SNS junctions, accounting for smooth variations in the order parameter.

Findings

Quantization rules for near-Fermi energy resonant states

Determination of resonance widths in imperfect junctions

Extension of scattering matrix models to smooth junction potentials

Abstract

We present a semi-classical analysis of the opening of superchannels in gated mesoscopic SNS junctions. For perfect junctions (i.e. hard-wall potential), this was considered by Chtchelkatchev, Lesovik and Blatter in the framework of scattering matrices. Here we allow for imperfections in the junction, so that the complex order parameter continues as a smooth function, which is a constant in the superconducting banks, and vanishes rapidly inside the lead. We obtain quantization rules for resonant Andreev states near energy E close to the Fermi level, including the determination of the resonance width.