Dependence of the intrinsic spin-Hall effect on spin-orbit interaction character

K. Nomura, Jairo Sinova, N. A. Sinitsyn, A. H. MacDonald

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55 Citations (Scopus)


We report on a comparative numerical study of the spin-Hall conductivity in two dimensions for three different spin-orbit interaction models; the standard k-linear Rashba model, the k-cubic Rashba model that describes two-dimensional hole systems, and a modified k-linear Rashba model in which the spin-orbit coupling strength is energy dependent. Numerical finite-size Kubo formula results indicate that the spin-Hall conductivity of the k-linear Rashba model vanishes for frequency ω much smaller than the scattering rate τ-1, with first-order relative fluctuations surviving out to large system sizes. For the k-cubic Rashba model case, the spin-Hall conductivity does not depend noticeably on ωτ and is finite in the dc limit, in agreement with experiment. For the modified k-linear Rashba model the spin-Hall conductivity is noticeably ωτ dependent but approaches a finite value in the dc limit. We discuss these results in the light of a spectral decomposition of the spin-Hall conductivity and associated sum rules, and in relation to a proposed separation of the spin-Hall conductivity into skew-scattering, intrinsic, and interband vertex correction contributions.

Original languageEnglish
Article number165316
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number16
Publication statusPublished - Oct 15 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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