Berry Phase Effects on Electronic Properties

TL;DR

This review discusses the profound influence of the Berry phase on electronic properties in solid state physics, highlighting its role in phenomena like Hall effects and ferroelectricity, and introduces semiclassical and re-quantization methods.

Contribution

It provides a comprehensive pedagogical overview of Berry phase effects in solid state physics, including new methods for semiclassical and quantum re-quantization approaches.

Findings

Berry phase influences various material properties

Semiclassical formulation aids in understanding electron dynamics

Re-quantization method bridges semiclassical and quantum theories

Abstract

Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.