2009 年 78 巻 10 号 p. 104714
A semiclassical model of the intrinsic spin-Hall effect (SHE) is presented which is relevant for a wide class of systems, including the two-dimensional electron gas with Rashba SOC. We start with a fully quantum mechanical treatment, introducing a gauge field formulation of the effect. Using this formulation as a basis, we construct an intuitive picture of the SHE, and derive general expressions for the spin-Hall current and conductivity. Finally, we propose an analogous effect in bilayer graphene systems.