Spin Hall conductivity of a disordered two-dimensional electron gas with Dresselhaus spin-orbit interaction

The spin Hall conductivity of a disordered two-dimensional electron gas has been investigated for a general spin-orbit interaction. We have found that in the diffusive regime of electron transport, the dc spin-Hall conductivity of a homogeneous system is zero due to impurity scattering when the spin-orbit coupling contains only the Rashba interaction, in agreement with existing results. However, when the Dresselhaus interaction is taken into account, the spin-Hall current is not zero. We also considered the spin-Hall currents induced by an inhomogeneous electric field. It is shown that a time-dependent electric charge induces a vortex of spin-Hall currents.