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

TL;DR

This paper derives boundary conditions for spin-charge diffusion at interfaces in 2D electron systems with Rashba spin-orbit coupling, revealing that spin density can be discontinuous and spin injection can be suppressed when mobility is constant.

Contribution

It introduces new boundary conditions for coupled spin-charge diffusion equations at interfaces with varying Rashba coupling in 2D systems.

Findings

Spin density is discontinuous at the interface.

Spin injection can be suppressed under certain conditions.

Boundary conditions depend on the change in Rashba coupling and mobility.

Abstract

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 $\alpha$, and an electric field parallel to the interface. We consider the limit where the spin-diffusion length l_s is long compared to the electron mean free path l, and assume that $\alpha$ changes discontinuously on the scale of l_s. We find that the spin density is also discontinuous on the scale of l_s. 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 $\alpha\neq0$ into a non-SO region with $\alpha=0$.