Microscopic polarization and magnetization fields in extended systems

TL;DR

This paper develops a lattice gauge approach to define microscopic polarization and magnetization fields in extended systems, enabling accurate optical response calculations that respect charge conservation and handle topologically nontrivial insulators.

Contribution

It introduces a novel microscopic framework for polarization and magnetization fields using a lattice gauge approach based on orthogonal orbitals and Green functions.

Findings

Recovers the limit of isolated atoms for distant sites.

Describes linear response of insulators, including topologically nontrivial ones.

Ensures charge conservation and avoids divergences in response calculations.

Abstract

We introduce microscopic polarization and magnetization fields at each site of an extended system, as well as free charge and current density fields associated with charge movement from site to site, by employing a lattice gauge approach based on a set of orthogonal orbitals associated with each site. These microscopic fields are defined using a single-particle electron Green function, and the equations governing its evolution under excitation by an electromagnetic field at arbitrary frequency involve the electric and magnetic fields rather than the scalar and vector potentials. If the sites are taken to be far from each other, we recover the limit of isolated atoms. For an infinite crystal we choose the orbitals to be maximally-localized Wannier functions, and in the long wavelength limit we recover the expected linear response of an insulator, including the zero frequency transverse conductivity of a topologically nontrivial insulator. For a topologically trivial insulator we recover the expected expressions for the macroscopic polarization and magnetization in the ground state, and find that the linear response to excitation at arbitrary frequency is described solely by the microscopic polarization and magnetization fields. For very general optical response calculations the microscopic fields necessarily satisfy charge conservation, even under basis truncation, and do not suffer from the false divergences at zero frequency that can plague response calculations using other approaches.