Effects of spin imbalance on the electric-field-driven quantum dissipationless spin current in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>-doped semiconductors

Abstract

It was proposed recently by Murakami et al. [Science 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.