Macroscopic Polarization from Electronic Wavefunctions

TL;DR

This paper discusses the modern theory of macroscopic polarization in extended electronic systems, emphasizing the Berry phase approach and recent advances for correlated and disordered systems, with implications for density functional theory.

Contribution

It presents a comprehensive, novel framework for understanding polarization in extended systems, including correlated and disordered cases, building on Berry phase concepts.

Findings

Polarization can be defined via Berry phase in extended systems.

Recent solutions enable polarization calculation in correlated/disordered systems.

The theory impacts the foundations of density functional theory.

Abstract

The dipole moment of any finite and neutral system, having a square-integrable wavefunction, is a well defined quantity. The same quantity is ill-defined for an extended system, whose wavefunction invariably obeys periodic (Born-von Karman) boundary conditions. Despite this fact, macroscopic polarization is a theoretically accessible quantity, for either uncorrelated or correlated many-electron systems: in both cases, polarization is a rather "exotic" observable. For an uncorrelated-either Hartree-Fock or Kohn-Sham-crystalline solid, polarization has been expressed and computed as a Berry phase of the Bloch orbitals (since 1993). The case of a correlated and/or disordered system received a definitive solution only very recently (1998): this latest development allows us present here the whole theory from a novel, and very general, viewpoint. The modern theory of polarization is even relevant to the foundations of density functional theory in extended systems.