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We report on a comparative numerical study of the spin Hall conductivity intwo-dimensions for three different spin-orbit interaction models; the standardk-linear Rashba model, the k-cubic Rashba model that describes two-dimensionalhole systems, and a modified k-linear Rashba model in which the spin-orbitcoupling strength is energy dependent. Numerical finite-size Kubo formularesults indicate that the spin Hall conductivity of the k-linear Rashba modelvanishes for frequency $\omega$ much smaller than the scattering rate$\tau^{-1}$, with order one relative fluctuations surviving out to large systemsizes. For the k-cubic Rashba model case, the spin Hall conductivity does notdepend noticeably on $\omega \tau$ and is finite in the {\em dc} limit, inagreement with experiment. For the modified k-linear Rashba model the spin Hallconductivity is noticeably $\omega \tau$ dependent but approaches a finitevalue in the {\em dc} limit. We discuss these results in the light of aspectral decomposition of the spin Hall conductivity and associated sum rules,and in relation to a proposed separation of the spin Hall conductivity intoskew-scattering, intrinsic, and interband vertex correction contributions.Comment: 10 pages, 4 figure

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