Spin Current and Polarization in Impure Two-Dimensional Electron Systems with Spin-Orbit Coupling

We derive the transport equations for two-dimensional electron systems with Rashba spin-orbit interaction and short-range spin-independent disorder. In the limit of slow spatial variations, we obtain coupled diffusion equations for the electron density and spin. Using these equations we calculate electric-field induced spin accumulation and spin current in a finite-size sample for an arbitrary ratio between spin-orbit energy splitting $\Delta$ and elastic scattering rate ${\tau }^{-1}$. We demonstrate that the spin-Hall conductivity vanishes in an infinite system independent of this ratio.

Figure 1

In a spin-Hall bar setup, the electric current is driven through 2DES contacted by the metallic leads connected to a voltage source. The electric field $E_x$ creates an in-plane spin polarization $S_y$ in the bulk. Spin currents $j_y^z$ are running in the vicinity of the contacts while vanishing in the bulk. Out-of-plane polarization $S_z$ is accumulated at the sample corners.