Physical Review B
The American Physical Society
Within the Kubo formalism, we estimate the spin-Hall conductivity in a two-dimensional electron gas with Rashba spin-orbit interaction and study its variation as a function of disorder strength and system size. The numerical algorithm employed in the calculation is based on the direct numerical integration of the time-dependent Schrödinger equation in a spin-dependent variant of the particle-source method. We ﬁnd that the spin-precession length Ls, controlled by the strength of the Rashba coupling, establishes the critical length scale that marks the signiﬁcant reduction of the spin-Hall conductivity in bulk systems. In contrast, the electron mean free path, inversely proportional to the strength of disorder, appears to have only a minor effect.
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