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

摘要

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