Superconducting phases and the second Josephson harmonic in tunnel junctions between diffusive superconductors

TL;DR

This paper develops a self-consistent perturbation theory for SIS Josephson junctions between diffusive superconductors, accurately calculating the second harmonic and refining the current-phase relation across all temperatures.

Contribution

It introduces a fully self-consistent perturbation approach that corrects previous models and explicitly computes the second Josephson harmonic in diffusive superconductor junctions.

Findings

Corrects previous results for the current-phase relation.

Calculates the second Josephson harmonic at arbitrary temperatures.

Describes phase differences between order parameter and Green functions.

Abstract

We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between the phases of the order parameter and of the anomalous Green functions.