Electrical spin orientation, spin-galvanic and spin-Hall effects in disordered two-dimensional systems

In disordered systems, the hopping conductivity regime is usually realized at low temperatures where spin-related phenomena differ strongly from the case of delocalized carriers. We develop the unified microscopic theory of current induced spin orientation, spin-galvanic and spin-Hall effects for the two-dimensional hopping regime. We show that the corresponding susceptibilities are proportional to each other and determined by the interplay between the drift and the diffusion spin currents. Estimations are made for realistic semiconductor heterostructures using the percolation theory. We show that the electrical spin polarization in the hopping regime increases exponentially with increase of the concentration of localization sites and may reach a few percents at the crossover from the hopping to the diffusion conductivity regime.