# Correspondence between bulk equilibrium spin-currents and edge spin accumulation in wires with spin-orbit coupling

## TL;DR

This paper reveals that in 1D wires with spin-orbit coupling, equilibrium spin currents cause edge spin accumulation perpendicular to the applied fields, with effects amplified in the superconducting state, generalizing Knight-shift theory.

## Contribution

It establishes a universal link between bulk equilibrium spin currents and edge spin accumulation in wires with spin-orbit coupling, including superconducting states.

## Key findings

- Edge spin polarization is perpendicular to both Zeeman and spin-orbit fields.
- Superconductivity enhances the transverse edge spin polarization.
- Transverse spin component at edges can be much larger than the parallel component.

## Abstract

We demonstrate that the interplay of Zeeman and spin-orbit coupling fields in a 1D wire leads to an equilibrium spin current that manifests itself in a spin accumulation at the wire ends with a polarization perpendicular to both fields. This is a universal property that occurs in the normal and superconducting state independently of the degree of disorder. We find that the edge spin polarization transverse to the Zeeman field is strongly enhanced in the superconducting state when the Zeeman energy is of the order of the superconducting gap. By calculating the space resolved magnetization response of the wire we demonstrate that the transverse component of the spin at the wire edges can be much larger than the one parallel to the field. This result generalizes the well established theory of the Knight-shift in superconductors to the case of finite systems.