Square-well model for superconducting pair-potential

TL;DR

This paper analyzes Andreev reflection in a one-dimensional square-well superconducting model, exploring current-phase relations and the roles of bound and continuum states, providing insights into inhomogeneous superconductivity.

Contribution

It introduces a detailed analysis of a square-well pair-potential model, including limiting cases, to enhance understanding of inhomogeneous superconductivity and superfluidity.

Findings

Current-phase relation expressed as a sum over Matsubara frequencies

Identification of bound and continuum level contributions to current

Model validity in specific cases and its foundational role

Abstract

We study Andreev reflection in a one-dimensional square-well pair-potential. We discuss the history of the model. The current-phase relation is presented as a sum over Matsubara frequencies. How the current arises from bound and continuum levels is found by analytic continuation. We discuss two limiting cases of the square-well potential, the zero-length well and the infinite well. The model is quantitatively valid in some cases but forms the basis for understanding a wide range of problems in inhomogeneous superconductivity and superfluidity.