Spin Hall effect due to intersubband-induced spin-orbit interaction in symmetric quantum wells

TL;DR

This paper explores the intrinsic spin Hall effect in symmetric quantum wells with two subbands, revealing a finite spin Hall conductivity influenced by intersubband-induced spin-orbit coupling, which varies with Fermi energy.

Contribution

It introduces a new intersubband-induced spin-orbit interaction mechanism and calculates its impact on the spin Hall conductivity in symmetric quantum wells.

Findings

Spin Hall conductivity remains finite at zero magnetic field when only the lowest subband is occupied.

The conductivity exhibits nonmonotonic behavior and can change sign with Fermi energy.

Realistic InSb quantum wells show measurable spin Hall effects due to this mechanism.

Abstract

We investigate the intrinsic spin Hall effect in two-dimensional electron gases in quantum wells with two subbands, where a new intersubband-induced spin-orbit coupling is operative. The bulk spin Hall conductivity $\sigma^z_{xy}$ is calculated in the ballistic limit within the standard Kubo formalism in the presence of a magnetic field $B$ and is found to remain finite in the B=0 limit, as long as only the lowest subband is occupied. Our calculated $\sigma^z_{xy}$ exhibits a nonmonotonic behavior and can change its sign as the Fermi energy (the carrier areal density $n_{2D}$) is varied between the subband edges. We determine the magnitude of $\sigma^z_{xy}$ for realistic InSb quantum wells by performing a self-consistent calculation of the intersubband-induced spin-orbit coupling.