Spin-orbit interaction in a two-dimensional electron gas: a SU(2) formulation

Spin-orbit interaction is usefully classified as extrinsic or intrinsic depending on its origin: the potential due to random impurities (extrinsic), or the crystalline potential associated with the band or device structure (intrinsic). In this paper we will show how by using a SU(2) formulation the two sources of spin-orbit interaction may be described in an elegant and unified way. As a result we obtain a simple description of the interplay of the two types of spin-orbit interaction, and a physically transparent explanation of the vanishing of the d.c. spin Hall conductivity in a Rashba two-dimensional electron gas when spin relaxation is neglected, and its reinstatement when spin relaxation is allowed. Furthermore, we obtain an explicit formula for the transverse spin polarization created by an electric current, which generalizes the standard formula obtained by Edelstein and Aronov and Lyanda-Geller by including extrinsic spin-orbit interaction and spin relaxation.