Electronic-structure theory of crystalline insulators under homogeneous electric field

TL;DR

This paper develops a theoretical framework extending Berry-phase polarization to describe the electronic structure of crystalline insulators under uniform electric fields, linking it with existing perturbation and computational methods.

Contribution

It introduces a novel approach based on energy band theory to analyze insulators in electric fields, extending Berry-phase polarization to nonzero fields.

Findings

Derived a polarization expression extending Berry-phase theory

Analyzed solution characteristics in electric fields

Connected with perturbation and computational schemes

Abstract

Based on the conventional energy band theory, an approach is presented to describe the electronic structure of crystalline insulators in the presence of a finite homogeneous electric field. The expression of polarization is derived which extends the ``Berry-phase'' theory of polarization to nonzero fields. The characteristics of the solutions are studied in details and the associations with the existing perturbation theories and computational schemes are discussed.