Numerical Study of the Spin Hall Conductance in the Luttinger Model
  We present first numerical studies of the disorder effect on the recently proposed intrinsic spin Hall conductance in a three dimensional (3D) lattice Luttinger model. The results show that the spin Hall conductance remains finite in a wide range of disorder strength, with large fluctuations. The disorder-configuration-averaged spin Hall conductance monotonically decreases with the increase of disorder strength and vanishes before the Anderson localization takes place. The finite-size effect is also discussed. 
W.Q. Chen, Z.Y. Weng, and D.N. Sheng