Boundary spin Hall effect in a two-dimensional semiconductor system with Rashba spin-orbit coupling

We derive boundary conditions for the coupled spin-charge diffusion equations at a transmitting interface between two-dimensional electron systems with different strengths of the Rashba spin-orbit (SO) coupling α and an electric field parallel to the interface. We consider the limit where the spin-diffusion length lₛ is long compared to the electron mean-free path l and assume that α changes discontinuously on the scale of lₛ. We find that the spin density is also discontinuous on the scale of lₛ. In the case where the electron mobility is constant across the interface, this leads to the complete suppression of the expected spin injection from a region with α≠0 into a non-SO region with α=0.