Interband Effects of Magnetic Field on Hall Effects for Dirac Electrons in Bismuth

Hall effects are investigated for three-dimensional Dirac electrons as a model of bismuth alloys. It is found that there is unconventional contributions to the Hall conductivity $\sigma_{xy}$ generated by the interband effects of a magnetic field. This phenomena is remarkable near the band-edge. The Hall coefficient exhibits two unexpected properties; a sharp peak at around the band-edges, and a drastic sign change in the band gap region. Implications of the present results to bismuth alloys are discussed.