Longitudinal and Spin-Hall Conductance of a Two-Dimensional Rashba System with Arbitrary Disorder

We calculate the longitudinal and spin-Hall conductances in four-lead bridges with Rashba-Dresselhaus spin-orbit interactions. Numerical results are obtained both within the Landauer-Büttiker formalism and by the direct evaluation of the Kubo formula. The microscopic Hamiltonian is obtained in the tight-binding approxi-mation in terms of the neareast-neighbor hopping integral t, the Rashba spin-orbit coupling VR, the Dresselhaus spin-orbit coupling VD, and an Anderson-type, on-site disorder energy strength W. We reconfirm that below a critical disorder threshold, the spin-Hall effect is present. Further, we study the effect on the two conductivities of the Fermi energy, Rashba and/or Dresselhaus coefficient ratio and system size