Spin Hall Effect in Doped Semiconductor Structures

In this Letter we present a microscopic theory of the extrinsic spin Hall effect based on the diagrammatic perturbation theory. Side-jump (SJ) and skew-scattering (SS) contributions are explicitly taken into account to calculate the spin Hall conductivity, and we show their effects scale as $σ_{xy}^{SJ}/σ_{xy}^{SS} \sim (\hbar/τ)/ε_F$, with $τ$ being the transport relaxation time. Motivated by recent experimental work we apply our theory to n- and p-doped 3D and 2D GaAs structures, obtaining $σ_s/σ_c \sim 10^{-3}-10^{-4}$ where $σ_{s(c)}$ is the spin Hall (charge) conductivity, which is in reasonable agreement with the recent experimental results of Kato \textit{et al}. [Science \textbf{306}, 1910 (2004)] in n-doped 3D GaAs system.

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