Intrinsic spin hall effect in the two-dimensional hole gas

We show that two types of spin-orbit coupling in the 2 dimensional holegas, with and without inversion symmetry breaking, contribute to the intrinsicspin-Hall effect. Furthermore, the vertex correction due to impurity scatteringvanishes in both cases, in sharp contrast to the case of usual Rashba couplingin the electron band. Recently, the spin-Hall effect in a hole doped GaAssemiconductor has been observed experimentally by Wunderlich et al. [Phys. Rev. Lett. 94, 047204 (2005).PRLTAO0031-900710.1103/PhysRevLett.94.047204]. From the factthat the lifetime broadening is smaller than the spin splitting, and the factimpurity vertex corrections vanish in this system, we argue that the observedspin-Hall effect should be in the intrinsic regime.