Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Abstract

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