Theory of Hall Conductivity and Its Exact Relationship to Orbital Magnetic Susceptibility

Abstract

A new formula for Hall conductivity is derived in terms of retarded and advanced Green’s functions. It contains transport and thermodynamic contributions and the latter is shown to be closely related to the orbital magnetic susceptibility. The physical interpretation of this relationship is clarified. By studying the Hall coefficient, it is also shown that the thermodynamic contribution becomes dominant at the band edge of the Dirac electron system, where the transport contribution decreases as the carrier density vanishes.