Spin-Hall Effect and Diamagnetism of Anisotropic Dirac Electrons in Solids

Abstract

Spin-Hall conductivity ${\sigma }_{\mathrm{s}xy}$ and orbital susceptibility $\chi$ are investigated for the anisotropic Wolff Hamiltonian, which is an effective Hamiltonian common to Dirac electrons in solids. It is found that, both for ${\sigma }_{\mathrm{s}xy}$ and $\chi$, the effect of anisotropy appears only in the prefactors, which is given as the Gaussian curvature of the energy dispersion, and their functional forms are equivalent to those of the isotropic Wolff Hamiltonian. As a result, it is revealed that the relationship between the spin Hall conductivity and the orbital susceptibility in the insulating state, ${\sigma }_{\mathrm{s}xy}=(3m{c}^2/\hslash e)\chi$, which was firstly derived for the isotropic Wolff Hamiltonian, is also valid for the anisotropic Wolff Hamiltonian. Based on this theoretical finding, the magnitude of spin-Hall conductivity is estimated for bismuth and its alloys with antimony by that of orbital susceptibility, which has good correspondence between theory and experiments. The magnitude of spin-Hall conductivity turns out to be as large as $e{\sigma }_{\mathrm{s}xy}\sim 10^4{\Omega }^{-1}{\mathrm{cm}}^{-1}$, which is about 100 times larger than that of Pt.

11 pages, 5 figures

References in corpus (7)

• Dissipationless Quantum Spin Current at Room Temperature
• Study of Intrinsic Spin Hall Effect and Orbital Hall Effect in 4d- and 5d- Transition Metals
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• Giant Intrinsic Spin and Orbital Hall Effects in Sr2MO4 (M=Ru,Rh,Mo)
• Interband Effects of Magnetic Field on Hall Effects for Dirac Electrons in Bismuth
• Spin-Hall Effect and Diamagnetism of Dirac Electrons
• Landau spectrum and twin boundaries of bismuth in the extreme quantum limit

Cited by in corpus (7)

• Transport Properties and Diamagnetism of Dirac Electrons in Bismuth
• Spin Pumping into Anisotropic Dirac Electrons
• Anisotropic spin Hall and spin Nernst effects in bismuth semimetal
• Anomalous Spin Transport Properties of Gapped Dirac Electrons with Tilting
• Local Observations of Orbital Diamagnetism and Excitation in Three-Dimensional Dirac Fermion Systems Bi${}_{1-x}$Sb${}_x$
• Characteristic singular behaviors of nodal line materials emerging in orbital magnetic susceptibility and Hall conductivity
• Impact of spin--orbit coupling on orbital diamagnetism in a narrow-gap semiconductor ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$