Ab initio calculation of the intrinsic spin Hall effect in semiconductors

Relativistic band theoretical calculations reveal that intrinsic spin Hall conductivity in hole-doped archetypical semiconductors Ge, GaAs, and AlAs is large [approximately 100(planck/e)(Omega cm)(-1)], showing the possibility of a spin Hall effect beyond the four-band Luttinger Hamiltonian. The calculated orbital-angular-momentum (orbital) Hall conductivity is one order of magnitude smaller, indicating no cancellation between the spin and orbital Hall effects in bulk semiconductors. Furthermore, it is found that the spin Hall effect can be strongly manipulated by strains, and that the ac spin Hall conductivity is large in pure as well as doped semiconductors.