Physical Review B
The American Physical Society
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.
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