Extrinsic Entwined with Intrinsic Spin Hall Effect in Disordered Mesoscopic Bars

TL;DR

This paper investigates the combined effects of extrinsic and intrinsic mechanisms on the spin Hall current in disordered 2DEGs, revealing complex behavior in the crossover regime with sample fluctuations and sign changes.

Contribution

It demonstrates that the spin Hall conductance in disordered 2DEGs results from a complex interplay of extrinsic and intrinsic effects, especially in the crossover transport regime.

Findings

Extrinsic contribution vanishes in weakly and strongly disordered limits.

Intrinsic contribution dominates in the quasiballistic limit.

In the crossover regime, conductance shows large fluctuations and sign changes.

Abstract

We show that pure spin Hall current, flowing out of a four-terminal phase-coherent two-dimensional electron gas (2DEG) within inversion asymmetric semiconductor heterostructure, contains contributions from both the extrinsic mechanisms (spin-orbit dependent scattering off impurities) and the intrinsic ones (due to the Rashba coupling). While the extrinsic contribution vanishes in the weakly and strongly disordered limits, and the intrinsic one dominates in the quasiballistic limit, in the crossover transport regime the spin Hall conductance, exhibiting sample-to-sample large fluctuations and sign change, is not simply reducible to either of the two mechanisms, which can be relevant for interpretation of experiments on dirty 2DEGs [V. Sih et al., Nature Phys. 1, 31 (2005)].