Inverse Spin Hall Effect and Anomalous Hall Effect in a Two-Dimensional Electron Gas

We study the coupled dynamics of spin and charge currents in a two-dimensional electron gas in the transport diffusive regime. For systems with inversion symmetry there are established relations between the spin Hall effect, the anomalous Hall effect and the inverse spin Hall effect. However, in two-dimensional electron gases of semiconductors like GaAs, inversion symmetry is broken so that the standard arguments do not apply. We demonstrate that in the presence of a Rashba type of spin-orbit coupling (broken structural inversion symmetry) the anomalous Hall effect, the spin Hall and inverse spin Hall effect are substantially different effects. Furthermore we discuss the inverse spin Hall effect for a two-dimensional electron gas with Rashba and Dresselhaus spin-orbit coupling; our results agree with a recent experiment.Comment: 5 page

Non-Abelian gauge fields in the gradient expansion: generalized Boltzmann and Eilenberger equations

We present a microscopic derivation of the generalized Boltzmann and Eilenberger equations in the presence of non-Abelian gauges, for the case of a non-relativistic disordered Fermi gas. A unified and symmetric treatment of the charge $[U(1)]$ and spin $[SU(2)]$ degrees of freedom is achieved. Within this framework, just as the $U(1)$ Lorentz force generates the Hall effect, so does its $SU(2)$ counterpart give rise to the spin Hall effect. Considering elastic and spin-independent disorder we obtain diffusion equations for charge and spin densities and show how the interplay between an in-plane magnetic field and a time dependent Rashba term generates in-plane charge currents.Comment: 11 pages, 1 figure; some corrections and updated/extended reference