Quantum kinetic equation for spin relaxation and spin Hall effect in GaAs

We present a general quantum kinetic theory of spin transport based on the Kadanoff- Baym equation (KBE), which we use to study dynamical spin processes in semiconductors right down to femtosecond and nanometer scales. In our application of KBE we describe the evolution of the non-equilibrium 2×2 matrix Green function for carrier spin, averaged over the thermal bath. Spin relaxation effects are treated within the Kadanoff-Baym Ansatz (KBA), while carrier interactions are treated within the random-phase model of screening. We track the detailed oscillation of the spin- polarized carrier state within the coherence time. Our general kinetic approach also allows description of the spin Hall effect when both impurity scattering and the Fröhlich interaction are included in the KBE collision term. We find that the level of spin current is very sensitive to the density of impurities, and that the Fröhlich interaction can generate a considerable spin current. Significantly, the Fröhlich term leads to a unique type of oscillatory behaviour in the spin current that is independent of impurity scattering effects.