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.

arXiv comment12 pages, 2 figures, submitted to J. Phys. Soc. Jpn

References in corpus (10)

• Anomalous Hall effect
• Universal Intrinsic Spin-Hall Effect
• Dissipationless Quantum Spin Current at Room Temperature
• Suppression of the Persistent Spin Hall Current by Defect Scattering
• Spin-Hall conductivity due to Rashba spin-orbit interaction in disordered systems
• 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
• Angle-resolved Landau spectrum of electrons and holes in bismuth
• Transport and spin conversion of multi-carriers in semimetal bismuth
• Spin-Hall Effect and Diamagnetism of Dirac Electrons

Cited by in corpus (12)

• The spin Hall effect of Bi-Sb alloys driven by thermally excited Dirac-like electrons
• Spin Hall effect driven by the spin magnetic moment current in Dirac materials
• Intrinsic orbital and spin Hall effect in bismuth semimetal
• Observation of gigantic spin conversion anisotropy in bismuth
• Spin Pumping into Anisotropic Dirac Electrons
• Seebeck effect of Dirac electrons
• Microscopic theory of spin Nernst effect
• Inverse Faraday effect in massive Dirac electrons
• Transport Coefficients of Dirac Ferromagnet: Effects of Vertex Corrections
• Microscopic origin of scalar potential induced topological transition in massive Dirac fermions and scalar Hall effect
• Temperature dependence of charge-to-spin conversion in rhombohedral (110) bismuth thin film
• Anisotropy of the spin Hall effect in a Dirac ferromagnet