Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Bismuth crystal is known for its noteworthy 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 since soon after the establishment of quantum mechanics, which was resolved eventually in 1970, on the basis of the effective Hamiltonian derived by Wolff, as being 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 the magneto-optic effect, of a system described by the Wolff Hamiltonian and its isotropic version with a special focus on exploring the possible relationship with orbital magnetism. It is shown that there is a fundamental relationship between the spin Hall conductivity and orbital susceptibility in the insulating state, and the possibility of a fully spin-polarized electric current in magneto-optics. Experimental tests of these interesting features have been proposed.