Universal spin-Hall conductance fluctuations in two dimensions

We report a theoretical investigation on spin-Hall conductance fluctuation of disordered four-terminal devices in the presence of Rashba or/and Dresselhaus spin-orbital interactions in two dimensions. As a function of disorder, the spin-Hall conductance G(sH) shows ballistic, diffusive, and insulating transport regimes. For given spin-orbit interactions, a universal spin-Hall conductance fluctuation (USCF) is found in the diffusive regime. The value of the USCF depends on the spin-orbit coupling t(so) but is independent of other system parameters. It is also independent of whether Rashba or Dresselhaus or both spin-orbital interactions are present. When t(so) is comparable to the hopping energy t, the USCF is a universal number similar to 0.18e/4 pi. The distribution of G(sH) crosses over from a Gaussian distribution in the metallic regime to a non-Gaussian distribution in the insulating regime as the disorder strength is increased.