Electric polarization and magnetization in metals

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 $T=0$ 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.

23 pages, 1 figure

References in corpus (9)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Orbital magnetization in periodic insulators
• Exponential localization of Wannier functions in insulators
• Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
• Theory of orbital magnetoelectric response
• Electric polarization in a Chern insulator
• Band theory of spatial dispersion in magnetoelectrics
• Pseudo-potentials based first-principles approach to the magneto-optical Kerr effect: from metals to the inclusion of local fields and excitonic effects
• Polarization and orbital magnetization in Chern insulators: A microscopic perspective

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• Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect
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