On Berry Phase in Bloch States

Abstract

We comment on the relation between Berry phase and quantized Hall conductivities for charge and spin currents in some Bloch states, such as Bloch electrons in the presence of electromagnetic fields and quasiparticles in the vortex states of superfluid $^3$He. One can find out that the arguments presented here are closely related to the spontaneous polarization in crystalline dielectrics and the adiabatic pumping.Comment: 2 pages, 1 figure, to be published in the proceedings of LT23 in Hiroshima, Aug. 200