Fluctuation contribution to Spin Hall Effect in Superconductors

TL;DR

This paper provides a theoretical analysis of how superconducting fluctuations influence spin Hall effects, revealing divergent behaviors and sign differences between extrinsic and intrinsic effects near the critical temperature.

Contribution

It is the first to analyze fluctuation contributions to both extrinsic and intrinsic spin Hall effects in superconductors, highlighting divergence patterns and sign changes.

Findings

Logarithmic divergence of fluctuation terms in 2D systems

Opposite sign of fluctuation effects on extrinsic spin Hall effect compared to normal state

Same sign of fluctuation effects on intrinsic spin Hall effect as in normal state

Abstract

We theoretically study the contribution of superconducting fluctuation to extrinsic spin Hall effects in two- and three-dimensional electron gas and intrinsic spin Hall effects in two-dimensional electron gas with Rashba-type spin-orbit interaction. The Aslamazov-Larkin, Density-of-States, Maki-Thompson terms have logarithmic divergence $\ln\epsilon$ in the limit $\epsilon=(T- T_{\mathrm{c}})/T_{\mathrm{c}} \rightarrow +0$ in two-dimensional systems for both extrinsic and intrinsic spin Hall effects except the Maki-Thompson terms in extrinsic effect, which are proportional to $(\epsilon-\gamma_\varphi)^{-1}\ln\epsilon$ with a cutoff $\gamma_\varphi$ in two-dimensional systems. We found that the fluctuation effects on the extrinsic spin Hall effect have an opposite sign to that in the normal state, while those on the intrinsic spin Hall effect have the same sign.