Numerical Study of Spin Hall Transport in a Two Dimensional Hole Gas System

TL;DR

This study numerically investigates the spin Hall effect in a disordered two-dimensional hole gas, revealing that while spin Hall conductance remains finite with disorder, intrinsic spin accumulation is suppressed, highlighting the role of spin conservation violations.

Contribution

It provides a detailed numerical analysis of spin Hall conductance and accumulation in disordered 2DHG systems, emphasizing the effects of disorder and spin conservation violations.

Findings

Spin Hall conductance remains finite with disorder in the thermodynamic limit.

Intrinsic spin Hall accumulation is suppressed by disorder.

Level crossing and spin-density oscillations occur without disorder.

Abstract

We present a numerical study of the spin Hall effect in a two-dimensional hole gas (2DHG) system in the presence of disorder. We find that the spin Hall conductance (SHC), extrapolated to the thermodynamic limit, remains finite in a wide range of disorder strengths for a closed system on torus. But there is no intrinsic spin Hall accumulation as induced by an external electric field once the disorder is turned on. The latter is examined by performing a Laughlin's Gedanken gauge experiment numerically with the adiabatical insertion of a flux quantum in a belt-shaped sample, in which the absence of level crossing is found under the disorder effect. Without disorder, on the other hand, energy levels do cross each other, which results in an oscillating spin-density-modulation at the sample boundary after the insertion of one flux quantum in the belt-shaped system. But the corresponding net spin transfer is only about one order of magnitude smaller than what is expected from the bulk SHC. These apparently contradictory results can be attributed to the violation of the spin conservation law in such a system. We also briefly address the dissipative Fermi surface contribution to spin polarization, which may be relevant to experimental measurements.