Effects of spin imbalance on the electric-field driven quantum dissipationless spin current in $p$-doped Semiconductors

TL;DR

This paper investigates how spin imbalance near the edges of p-doped semiconductors affects the intrinsic spin Hall effect, revealing that spin Hall conductivity varies with position and requires microscopic modeling for accurate description.

Contribution

It provides a microscopic analysis of spin imbalance effects on the quantum dissipationless spin current in p-doped semiconductors, highlighting position-dependent spin Hall conductivity.

Findings

Spin imbalance causes position-dependent spin Hall conductivity.

Microscopic calculations are necessary for accurate spin current and accumulation modeling.

Edge effects significantly influence the intrinsic spin Hall effect.

Abstract

It was proposed recently by Murakami et al. [Science \textbf{301}, 1348(2003)] that in a large class of $p$-doped semiconductors, an applied electric field can drive a quantum dissipationless spin current in the direction perpendicular to the electric field. In this paper we investigate the effects of spin imbalance on this intrinsic $spin$ Hall effect. We show that in a real sample with boundaries, due to the presence of spin imbalance near the edges of the sample, the spin Hall conductivity is not a constant but a sensitively $position$-$dependent$ quantity, and due to this fact, in order to take the effects of spin imbalance properly into account, a microscopic calculation of both the quantum dissipationless spin Hall current and the spin accumulation on an equal footing is thus required. Based on such a microscopic calculation, a detailed discussion of the effects of spin imbalance on the intrinsic spin Hall effect in thin slabs of $p$-doped semiconductors are presented.