Berry phase and quantized Hall effect in three-dimension

Abstract

We consider Bloch electrons in the electromagnetic field and argue the relation between the Berry phase and the quantized Hall conductivity in three-dimension. The Berry phase we consider here is induced by the adiabatic change of the time-dependent vector potential. The relation has been shown in two-dimensional systems, and we generalize the relation in three-dimensional systems.Comment: corrected some typos. Accepted for publication in J. Phys. Soc. Jp