Spin-Hall effect and spin coherent waves in semiconductors with Rashba spin-orbit interaction

Based on rigorous quantum-kinetic equations for the spin-density matrix, spin-charge coupled drift-diffusion equations are derived for a strongly confined two-dimensional hole gas. An electric field leads to a coupling between the spin and charge degrees of freedom. For weak spin-orbit interaction, this coupling gives rise to the intrinsic spin-Hall effect that occurs in the diffusive regime. There exists a threshold value of the spin-orbit coupling constant that separates spin diffusion from ballistic spin transport. In the latter regime, undamped spin-coherent oscillations are observed. Their relationship to the zitterbewegung is discussed. The analytic results are compared with an exact microscopic approach valid in the ballistic regime. (c) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.