Josephson effect in multi-terminal superconductor-ferromagnet junctions coupled via triplet components

TL;DR

This paper investigates the Josephson effect in multi-terminal superconductor-ferromagnet junctions with triplet components, revealing unique current-phase relations, the influence of spin orientations, and temperature-dependent behaviors of the critical current.

Contribution

It introduces a general formula for the Josephson current in multi-terminal junctions with triplet components and analyzes different configurations, highlighting novel effects of spin orientations and additional singlet superconductors.

Findings

No interaction between antiparallel triplet pairs.

Unusual current-phase relation with an added singlet superconductor.

Nonmonotonic temperature dependence of critical current.

Abstract

On the basis of the Usadel equation we study a multi-terminal Josephson junction. This junction is composed by "magnetic" superconductors S$_{\text{m}}$ which have singlet pairing and are separated from the normal n~wire by spin filters so that the Josephson coupling is caused only by fully polarized triplet components. We show that there is no interaction between triplet Cooper pairs with antiparallel total spin orientations. The presence of an additional singlet superconductor S attached to the n wire leads to a finite Josephson current $I_{\text{Q}}$ with an unusual current--phase relation. The density of states in the n wire for different orientations of spins of Cooper pairs is calculated. We derive a general formula for the current $I_{\text{Q}}$ in a multi-terminal Josephson contact and apply this formula for analysis of two four-terminal Josephson junctions of different structures. It is shown in particular that both the "nematic" and the "magnetic" cases can be realized in these junctions. In a two-terminal structure with parallel filter orientations and in a three-terminal structure with antiparallel filter orientations of the "magnetic" superconductors with attached additional singlet superconductor, we find a nonmonotonic temperature dependence of the critical current. Also, in these structures, the critical current shows a Riedel peak like dependence on the exchange field in the "magnetic" superconductors. Although there is no current through the S/n interface due to orthogonality of the singlet and triplet components, the phase of the order parameter in the superconuctor S is shown to affect the Josephson current in a multi-terminal structure.