Spin Hall Conductivity in the impure two-dimensional Rashba s-wave superconductor

TL;DR

This paper calculates the spin Hall conductivity in a 2D Rashba s-wave superconductor with impurities, revealing how it varies with superconducting gap, impurity concentration, and temperature, and showing it becomes zero in certain limits.

Contribution

It provides a detailed analysis of how impurity scattering and superconducting gap influence the spin Hall conductivity in 2D Rashba superconductors, including new insights into the clean and dirty limits.

Findings

SHC decreases monotonically with increasing superconducting gap.

In the dirty limit, SHC vanishes; it depends on gap and impurity concentration.

SHC is independent of spin-orbit coupling in the clean limit.

Abstract

Based on the Kubo formula approach, the spin Hall conductivity (SHC) of a two-dimensional (2D) Rashba s-wave superconductor in the presence of nonmagnetic impurities is calculated. We will show that by increasing the superconducting gap, the SHC decreases monotonically to zero, while by decreasing the concentration of impurities at zero gap, the SHC closes to the clean limit universal value . As a function of the impurity relaxation rate at and (is the spin-orbit coupling in unit of), we will show that in the dirty limit () the SHC vanishes, and by increasing the relaxation time () the SHC depends on the value of superconducting gap (), is changed from zero for full gap to in zero gap. At low temperatures, the SHC goes to zero exponentially and near the critical temperature depending on the concentration of the scattering centers, the SHC will tend to the value of normal state. We will also show that the SHC is independent of spin-orbit coupling () in the clean limit.