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Electric polarization and magnetization in metals

by P. T. Mahon, J. E. Sipe

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Submission summary

Authors (as registered SciPost users): Perry Mahon
Submission information
Preprint Link: scipost_202206_00031v3  (pdf)
Date accepted: 2022-12-23
Date submitted: 2022-12-16 16:58
Submitted by: Mahon, Perry
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


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=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 density of free carriers vanishes and a trivial insulator results, our expressions reduce to those expected for the unperturbed polarization and magnetization, and the electric susceptibility.

List of changes

In response to the referees comments we have made the following changes:
- We have added the “mixed” form of (24) above it as an unnumbered equation as well as the text beginning “Although the matrix elements appearing in …” just before the start of Sec. III A.
- We have also added the footnote beginning with "For example, in the linear response of a “topologically trivial” insulator, ...".
- We have added references to the publications PRB 82 035104, PRB 95 155203, and PRB 86 125139
- We have modified the sentence beginning with "To simplify these initial considerations we here neglect local field corrections, ...".

Published as SciPost Phys. 14, 058 (2023)

Reports on this Submission

Anonymous Report 1 on 2022-12-17 (Invited Report)


Dear editor,

I thank the authors for their answers to me questions and comments and for the second revision of the manuscript.
I think the manuscript can now be accepted an article in SciPost Physics.

  • validity: -
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