Spin-Hall Effect in Two-Diensional Spin-Orbit Coupled Systems with Disorder

The spin-Hall conductance of a two-dimensional electron system with the Rashba spin-orbit coupling and disorder is calculated numerically by using the Landauer-B\"{u}ttiker formula and Green's function approach. We find that the spin-Hall conductance can be much greater or smaller than the universal value $e/8\pi$, depending on the magnitude of the SO coupling, the electron Fermi energy and the disorder strength. The spin-Hall conductance does not vanish with increasing sample size for a wide range of disorder strength. The position-dependent spin polarization is also calculated. Our result is consistent with recent experimental observation of spin polarization near the edges of a semiconductor channel detected and imaged by using Kerr rotation microscopy.