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Bismuth crystal is known for its remarkable properties resulting fromparticular electronic states, e. g., the Shubnikov-de Haas effect and the deHaas-van Alphen effect. Above all, the large diamagnetism of bismuth had been along-standing puzzle soon after the establishment of quantum mechanics, whichhad been resolved eventually in 1970 based on the effective Hamiltonian derivedby Wolff as due to the interband effects of a magnetic field in the presence ofa large spin-orbit interaction. This Hamiltonian is essentially the same as theDirac Hamiltonian, but with spatial anisotropy and an effective velocity muchsmaller than the light velocity. This paper reviews recent progress in thetheoretical understanding of transport and optical properties, such as theweak-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 aspecial interest of exploring possible relationship with orbital magnetism. Itis shown that there exist a fundamental relationship between spin Hallconductivity 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.

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth