Interband Contributions from the Magnetic Field on Hall Effects for Dirac Electrons in Bismuth

The Hall conductivity sigmaxy of Dirac electrons with a spin-orbit interaction is examined. It is shown that there is an unconventional contribution to sigmaxy generated by the interband effects of a magnetic field, which is remarkable near the band edges and does not depend on impurity scatterings so much, suggesting the same origin as the known large diamagnetism. Correspondingly, the Hall coefficient exhibits unexpected peaks at around the band edges. Implications of the present results to bismuth alloys are discussed.