Microscopic polarization and magnetization fields in extended systems

Perry T. Mahon, Rodrigo A. Muniz, and J. E. Sipe
Phys. Rev. B 99, 235140 – Published 20 June 2019

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.

  • Received 9 November 2018
  • Revised 18 March 2019

DOI:https://doi.org/10.1103/PhysRevB.99.235140

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Perry T. Mahon1,*, Rodrigo A. Muniz1,2,†, and J. E. Sipe1,‡

  • 1Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
  • 2Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109, USA

  • *pmahon@physics.utoronto.ca
  • rodrigo.a.muniz@gmail.com
  • sipe@physics.utoronto.ca

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Issue

Vol. 99, Iss. 23 — 15 June 2019

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