Intrinsic and Extrinsic Spin Hall Effects of Dirac Electrons

Abstract

We investigate the spin Hall effect (SHE) of electrons described by the Dirac equation, which is used as an effective model near the $L$-points in bismuth. By considering short-range nonmagnetic impurities, we calculate the extrinsic as well as intrinsic contributions on an equal footing. The vertex corrections are taken into account within the ladder type and the so-called skew-scattering type. The intrinsic SHE which we obtain is consistent with that of Fuseya et al. [J. Phys. Soc. Jpn. 81, 93704 (2012)]. It is found that the extrinsic contribution dominates the intrinsic one when the system is (semi)metallic. The extrinsic SHE due to the skew scattering is proportional to $\Delta /n_{\mathrm{i}}u$, where $2\Delta$ is the band gap, $n_{\mathrm{i}}$ is the impurity concentration, and $u$ is the strength of the impurity potential.

12 pages, 2 figures, submitted to J. Phys. Soc. Jpn

References in corpus (4)

• Dissipationless Quantum Spin Current at Room Temperature
• Transport Properties and Diamagnetism of Dirac Electrons in Bismuth
• Vertex Corrections on the Anomalous Hall Effect in Spin-polarized Two-dimensional Electron Gases with Rashba Spin-orbit Interaction
• Spin-Hall Effect and Diamagnetism of Dirac Electrons