Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

TL;DR

This paper reviews recent theoretical advances in understanding the transport and magnetic properties of Dirac electrons in bismuth, highlighting their relation to spin Hall effects, orbital magnetism, and potential for spin-polarized currents.

Contribution

It provides a comprehensive review of the transport and optical properties of Dirac electrons in bismuth based on the Wolff Hamiltonian, linking spin Hall conductivity with orbital susceptibility.

Findings

Existence of a fundamental relationship between spin Hall conductivity and orbital susceptibility.

Potential for fully spin-polarized electric currents in magneto-optics.

Proposed experimental tests for these phenomena.

Abstract

Bismuth crystal is known for its remarkable properties resulting from particular electronic states, e. g., the Shubnikov-de Haas effect and the de Haas-van Alphen effect. Above all, the large diamagnetism of bismuth had been a long-standing puzzle soon after the establishment of quantum mechanics, which had been resolved eventually in 1970 based on the effective Hamiltonian derived by Wolff as due to the interband effects of a magnetic field in the presence of a large spin-orbit interaction. This Hamiltonian is essentially the same as the Dirac Hamiltonian, but with spatial anisotropy and an effective velocity much smaller than the light velocity. This paper reviews recent progress in the theoretical understanding of transport and optical properties, such as the weak-field Hall effect together with the spin Hall effect, and ac conductivity, of a system described by the Wolff Hamiltonian and its isotropic version with a special interest of exploring possible relationship with orbital magnetism. It is shown that there exist a fundamental relationship between spin Hall conductivity and orbital susceptibility in the insulating state on one hand, and the possibility of fully spin-polarized electric current in magneto-optics. Experimental tests of these interesting features have been proposed.