Theory of diffusive {\phi}0 Josephson junctions in the presence of spin-orbit coupling

TL;DR

This paper develops a microscopic theory for diffusive Josephson junctions with spin-orbit coupling, revealing a finite intrinsic phase difference influenced by spin fields and SOC, with analytical and numerical insights.

Contribution

It introduces a comprehensive SU(2) covariant quasiclassical framework to analyze the phase behavior of diffusive SNS junctions with spin-orbit coupling and spin-splitting fields.

Findings

Finite intrinsic phase difference  <  between superconductors when both h and SOC are finite

Analytical and numerical results for  as a function of spin field strength, junction length, temperature, and interface properties

Demonstration of  dependence on Rashba SOC parameters

Abstract

We present a full microscopic theory based on the SU(2) covariant formulation of the quasiclassical formalism to describe the Josephson current through an extended superconductor-normal metal- superconductor (SNS) diffusive junction with an intrinsic spin-orbit coupling (SOC) in the presence of a spin-splitting field h. We demonstrate that the ground state of the junction corresponds to a finite intrinsic phase difference 0 < {\phi}0 < 2{\pi} between the superconductor electrodes provided that both, h and the SOC-induced SU(2) Lorentz force are finite. In the particular case of a Rashba SOC we present analytic and numerical results for {\phi}0 as a function of the strengths of the spin fields, the length of the junction, the temperature and the properties of SN interfaces.