Spin Hall effect in infinitely large and finite-size diffusive Rashba two-dimensional electron systems: A helicity-basis nonequilibrium Green's function approach

Details Spin Hall effect in infinitely large and finite-size diffusive Rashba two-dimensional electron systems: A helicity-basis nonequilibrium Green's function approach Spin Hall effect in infinitely large and finite-size diffusive Rashba two-dimensional electron systems: A helicity-basis nonequilibrium Green's function approach

2006-05-28

arxiv.org/abs/cond-mat/0605687v1

Phys. Rev. B 73, 205327 (2006)

Physics

Condensed Matter

Materials Science

9 pages, 3 figures, extended version of cond-mat/0411629

Scientific paper

10.1103/PhysRevB.73.205327

A nonequilibrium Green's function approach is employed to investigate the spin-Hall effect in diffusive two-dimensional electron systems with Rashba spin-orbit interaction. Considering a long-range electron-impurity scattering potential in the self-consistent Born approximation, we find that the spin-Hall effect arises from two distinct interband polarizations in helicity basis: a disorder-unrelated polarization directly induced by the electric field and a polarization mediated by electron-impurity scattering. The disorder-unrelated polarization is associated with all electron states below the Fermi surface and produces the original intrinsic spin-Hall current, while the disorder-mediated polarization emerges with contribution from the electron states near the Fermi surface and gives rise to an additional contribution to the spin-Hall current. Within the diffusive regime, the total spin-Hall conductivity vanishes in {\it infinitely large} samples, independently of temperature, of the spin-orbit coupling constant, of the impurity density, and of the specific form of the electron-impurity scattering potential. However, in a {\it finite-size} Rashba two-dimensional semiconductor, the spin-Hall conductivity no longer always vanishes. Depending on the sample size in the micrometer range, it can be positive, zero or negative with a maximum absolute value reaching as large as $e/8\pi$ order of magnitude at low temperatures. As the sample size increases, the total spin-Hall conductivity oscillates with a decreasing amplitude. We also discuss the temperature dependence of the spin-Hall conductivity for different sample sizes.

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