Microscopic Theory of Superconductor-Constriction-Superconductor Josephson Junctions in a Magnetic Field

TL;DR

This paper presents a detailed microscopic analysis of superconductor-constriction-superconductor Josephson junctions under magnetic fields, revealing how temperature, geometry, and magnetic effects influence Andreev states and the Josephson effect.

Contribution

It provides the first self-consistent numerical solutions of the Eilenberger equations for these junctions, including magnetic fields and geometric effects.

Findings

Andreev bound states develop substructure with supercurrent flow

Josephson effect is independent of $$ when penetration depth is large

Weak link shows minimal sensitivity to external magnetic fields

Abstract

Self-consistent solutions of microscopic Eilenberger theory are presented for a two-dimensional model of a superconducting channel with a geometric constriction. Magnetic fields, external ones as well as those caused by the supercurrents, are included and the relevant equations are solved numerically without further assumptions. Results concerning the influence of temperature, geometric parameters, of $\kappa=\lambda_L/\xi_0$ and of external magnetic fields on the Andreev bound states in the weak link and on the current-phase relation are presented. We find that the Andreev bound states within the junction obtain peculiar substructure when a finite supercurrent flows. As long as the London penetration depth is comparable to or bigger than the extension of the constriction, the Josephson effect is independent of $\kappa$. Furthermore, the weak link is very insensitive to external magnetic fields. Features restricted to a self-consistent calculation are discussed.