Non-equilibrium spin transport in Zeeman-split superconductors

TL;DR

This paper theoretically explores non-local conductance in Zeeman-split superconductors, revealing that the observed signals can be attributed to thermoelectric effects rather than solely spin imbalance.

Contribution

It introduces a theoretical framework for understanding non-local conductance in Zeeman-split superconductors, considering models of quasiparticle equilibration and proposing an alternative interpretation of experimental signals.

Findings

Non-local conductance persists over distances larger than charge and spin relaxation lengths.

The non-local signal can be explained as a thermoelectric effect, not just spin imbalance.

Theoretical models match recent experimental observations.

Abstract

We investigate theoretically the non-local conductance through a superconducting wire in tunnel contact with normal and ferromagnetic leads. In the presence of an in-plane magnetic field, the superconducting density of states is spin-split, and the current injected from the normal lead is spin-polarized. A non-local conductance that is antisymmetric with the applied voltage can be measured with a ferromagnetic lead. It persists for a distance between the contacts that is larger than both the charge-imbalance relaxation length and the normal-state spin relaxation length. We determine its amplitude by considering two extreme models of weak and strong internal equilibration of the superconducting quasiparticles due to electron-electron interactions. We find that the non-local signal, which was measured in recent experiments and discussed as a spin-imbalance effect, can be interpreted alternatively as the signature of a thermoelectric effect.