Zeeman and spin–orbit effects on the spin-Hall conductance

We show that when a two-dimensional interacting electron gas is submitted to a perpendicular magnetic field, the application of an in-plane electric field E induces a spin current perpendicular to E whose conductivity is quantized. This current can lead to spin accumulation that might be detected by means of optical experiments. The appearance of this intrinsic spin-Hall effect is crucially based on the validity of Kohnʹs theorem and on the presence of the Zeeman term in the electron Hamiltonian. The possibility of resonant effects in the spin-Hall conductivity due to the combined effect of Rashba and Dresselhaus spin–orbit couplings is discussed.