The spin Hall effect provides a new possible way to effectively inject spins into paramagnetic semiconductors. Here, we investigate the spin-Hall effect in a p-type Luttinger semiconductor employing a two-band kinetic equation analysis. The long-range disorder effect on spin-Hall current (SHC) is considered within the self-consistent Born approximation. We find that in addition to the intrinsic SHC proposed previously, there is a nonvanishing SHC that originates from long-range electron-impurity scattering, but which is independent of impurity density in the diffusive regime. This SHC has an opposite sign from the intrinsic one, leading to a significant reduction of the total SHC. We also carry out a numerical analysis of the hole density dependencies of SHC and spin mobility, finding that with increasing hole density, the SHC first increases and then falls, while the spin mobility monotonically decreases.
Quantum oscillations, magnetic breakdown and thermal Hall effect in Co3Sn2S2