Spin Hall effect and Berry phase in two-dimensional electron gas

The spin Hall effect is investigated in a high mobility two-dimensional electron system with the spin-orbital coupling of both the Rashba and the Dresselhaus types. A spin current perpendicular to the electric field is generated by either the Rashba or the Dresselhaus coupling. The spin Hall conductance is independent of the stength of the coupling, but its sign is determined by the relative ratio of the two couplings. The direction of spin current is controllable by tuning the magnitude of the surface electric field perpendicular to the two-dimensional plane via adjusting the Rashba coupling. It is observed that the spin Hall conductance has a close relation to the Berry phase of conduction electrons.