Asymptotic behavior of spin Hall conductance in mesoscopic two-dimensional electron systems

The spin Hall conductance (SHC) in four-terminal junction systems with Rashba spin-orbit coupling is investigated numerically with main focus on the case where the electron Fermi energy is near the tight-binding band bottom. The SHC oscillates at small sample sizes, and the oscillation amplitude decreases with increasing sample size. The origin of the oscillations in the SHC is discussed. When the sample size L becomes sufficiently large, the SHC shows asymptotic trend to increase with sample size, even in the presence of weak disorder. The SHC may possibly become much greater than the universal value e/8π. Our results suggest that the spin Hall effect in mesoscopic systems has different origin from that in bulk systems.