Spin Hall effect in a diffusive two-dimensional electron gas in the presence of both extrinsic and intrinsic spin-orbit coupling

A microscopic theory of the spin Hall effect in a diffusive two-dimensional electron gas in the presence of both extrinsic spin-orbit coupling (due to spin-orbit dependent impurity scatterings) and $k$-linear intrinsic spin-orbit coupling (due to spin-orbit splitting of the conduction band) is developed. We show that the spin Hall effect in the presence of both extrinsic and $k$-linear intrinsic spin-orbit coupling has basically an extrinsic origin from the theoretical points of view, but due to the interplay of extrinsic and intrinsic spin-orbit coupling, it may exhibit some interesting new features that were not found in the usual extrinsic or the usual intrinsic spin Hall effect.