On Berry Phase in Bloch States

TL;DR

This paper explores the connection between Berry phase and quantized Hall conductivities in various Bloch states, highlighting their relation to phenomena like polarization and adiabatic pumping.

Contribution

It provides insights into the relationship between Berry phase and Hall conductivities in Bloch states, linking it to polarization and adiabatic processes.

Findings

Berry phase relates to quantized Hall conductivities in Bloch states

Connections to spontaneous polarization in dielectrics

Implications for adiabatic pumping phenomena

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.