Inter-band effects of magnetic field on orbital susceptibility and Hall conductivity – case of bismuth


  • In commemoration of Paul Drude (1863–1906)


Interband effects of magnetic field on oribital susceptibility and Hall conductivity have been theoretically studied with special reference to single crystal bismuth (Bi), whose energy bands near the band-edges are similar to those of Dirac electrons. It has long been known that orbital susceptibilty in Bi has a maximum when the Fermi energy is located in the band-gap and then the density of states at the Fermi energy is vanishing. This implies that the magnetic field induces persisitint current even in the insulating state. On the other hand, weak-field Hall conducctivity, which reflects transport current, has turned out to be vanishing if the Fermi energy is in the band-gap. Interesting possibility has been pointed out of the inter-band contributions to the Hall conductivity once the Fermi energy lies slightly in the energy band.