Spin polarization of Bloch states and Hall currents in GaAs quantum wells

Real-space distribution of the Hall current densities and their spin polarization in non-magnetic zinc-blende semiconductors is analysed. It is shown that the applied current gives rise to a local spin polarization accompanied by spin-polarized Hall-current densities. Especially for hole carriers they are responsible for transferring spins of different orientation in opposite directions, spin Hall current, while the total Hall current vanishes.