Time evolution of coherent wave propagation and spin relaxation in spin-orbit coupled systems

We investigate, both numerically and analytically, the time evolution of a particle in an initial plane wave state as it is subject to elastic scattering in a two-dimensional disordered system with Rashba spin-orbit coupling (SOC). In the analytic calculation, we treat the SOC non-perturbatively, and the disorder perturbatively using the Diffuson and the Cooperon. We calculate the time dependence of coherent backscattering (CBS) as a function of the strength of the SOC. We identify weak and strong SOC regimes, and give the relevant time and energy scales in each case. By studying the time dependence of the anisotropy of the disorder-averaged momentum distribution we identify the spin relaxation time. We find a crossover from D'yakonov-Perel' spin relaxation for weak SOC to Elliot-Yafet like behaviour for strong SOC.