Affiliation:
1. University of Toronto
2. The University of Texas at Austin
Abstract
A feature of the “modern theory” is that electric polarization is not
well-defined in a metallic ground state. A different approach invokes
the general existence of a complete set of exponentially localized
Wannier functions, with respect to which general definitions of
microscopic electronic polarization and magnetization fields, and free
charge and current densities are always admitted. These definitions
assume no particular initial electronic state of the crystal, and the
set of microscopic fields satisfy the usual relations of classical
electrodynamics. Notably, when applied to a trivial insulator initially
occupying its T=0T=0
ground state, the expressions for the unperturbed polarization and
orbital magnetization, and for the orbital magnetoelectric
polarizability tensor obtained from these different approaches can
agree. However, the “modern theory of magnetization” has been extended
via thermodynamic arguments to include metals and Chern insulators. We
here compare with that generalization and find disagreement; the manner
in which the expressions differ elucidates the distinct philosophies of
these approaches. Our approach leads to the usual electrical
conductivity tensor in the long-wavelength limit; in the absence of any
scattering mechanisms, the dc divergence of that tensor is due to the
free current density and the finite-frequency generalization of the
anomalous Hall contribution arises from a combination of bound and free
current densities. As well, in the limit that the electronic ground
state is that of a trivial insulator, our expressions reduce to those
expected for the unperturbed polarization and magnetization, and the
electric susceptibility.
Funder
Government of Ontario
Natural Sciences and Engineering Research Council
Subject
General Physics and Astronomy