Generation of spin current and polarization under dynamic gate control   of spin-orbit interaction in low-dimensional semiconductor systems
  Based on the Keldysh formalism, the Boltzmann kinetic equation and the drift diffusion equation have been derived for studying spin polarization flow and spin accumulation under effect of the time dependent Rashba spin-orbit interaction in a semiconductor quantum well. The time dependent Rashba interaction is provided by time dependent electric gates of appropriate shapes. Several examples of spin manipulation by gates have been considered. Mechanisms and conditions for obtaining the stationary spin density and the induced rectified DC spin current are studied. 
C. S. Tang, A. G. Mal'shukov, and K. A. Chao