Nonsinusoidal current-phase relations and the $0-\pi$ transition in diffusive ferromagnetic Josephson junctions

TL;DR

This paper investigates how interfacial transparency affects the current-phase relation and 0-π transition in diffusive ferromagnetic Josephson junctions, revealing nonsinusoidal behavior and small residual supercurrents near transition points.

Contribution

It provides a theoretical analysis of the impact of finite interfacial transparency on Josephson current-phase relations and 0-π transitions, aligning with recent experimental observations.

Findings

Current-phase relation becomes nonsinusoidal at finite transparency.

Weak interfacial disorder introduces a second-harmonic component.

Residual supercurrent can be significant at the 0-π transition.

Abstract

We study the effect of the interfacial transparency on the Josephson current in a diffusive ferromagnetic contact between two superconductors. In contrast to the cases of the fully transparent and the low-transparency interfaces, the current-phase relation is shown to be nonsinusoidal for a finite transparency. It is demonstrated that even for the nearly fully transparent interfaces the small corrections due to weak interfacial disorders contribute a small second-harmonic component in the current-phase relation. For a certain thicknesses of the ferromagnetic contact and the exchange field this can lead to a tiny minimum supercurrent at the crossover between 0 and $\pi$ states of the junction. Our theory has a satisfactory agreement with the recent experiments in which a finite supercurrent was observed at the transition temperature. We further explain the possibility for observation of a large residual supercurrent if the interfaces have an intermediate transparency.