Extrinsic Spin-Charge Coupling in Diffusive Superconducting Systems

TL;DR

This paper develops a theoretical framework for diffusive superconductors with extrinsic spin-orbit coupling, revealing a new spin-orbit torque term unique to the superconducting state that enables novel spintronic effects.

Contribution

It derives a diffusion equation incorporating a previously unknown spin-orbit torque term specific to superconductors, expanding understanding of spin-charge interactions in these systems.

Findings

Identification of a new spin-orbit torque term in superconductors.

Expression of spin-orbit effects via three kinetic coefficients.

Qualitative analysis of spin torque in a magnetic vortex with triplet correlations.

Abstract

We present a theoretical study of diffusive superconducting systems with extrinsic spin-orbit coupling and arbitrarily strong impurity potential. We derive from a microscopic Hamiltonian a diffusion equation for the quasi-classical Green function, and demonstrate that all mechanisms related to the spin-orbit coupling are expressed in terms of three kinetic coefficients: the spin Hall angle, the spin current swapping coefficient, and the spin relaxation rate due to Elliott-Yafet mechanism. The derived diffusion equation contains a hitherto unknown term describing a spin-orbit torque that appears exclusively in the superconducting state. As an example, we provide a qualitative description of a magnetic vortex in a superconductor with triplet correlations, and show that the novel term describes a spin torque proportional to the vector product between the spectral angular momentum of the condensate and the triplet vector. Our equation opens up the possibility to explore spintronic effects in superconductors with no counterparts in the normal metallic state.