Spin Hall Effect in Doped Semiconductor Structures

TL;DR

This paper develops a microscopic theory for the extrinsic spin Hall effect in doped semiconductors, explicitly including side-jump and skew-scattering contributions, and applies it to GaAs structures, aligning well with recent experiments.

Contribution

It provides a detailed microscopic calculation of the extrinsic spin Hall effect, incorporating both side-jump and skew-scattering mechanisms, and applies the theory to real doped semiconductor structures.

Findings

Calculated spin Hall conductivity in GaAs structures matches experimental data.

Identified the scaling relationship between side-jump and skew-scattering contributions.

Estimated spin Hall to charge conductivity ratio in doped GaAs.

Abstract

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 $\sigma_{xy}^{SJ}/\sigma_{xy}^{SS} \sim (\hbar/\tau)/\epsilon_F$, with $\tau$ 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 $\sigma_s/\sigma_c \sim 10^{-3}-10^{-4}$ where $\sigma_{s(c)}$ 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.