Abstract
We extend a field theoretic approach for the investigation of the electronic charge-current density response of crystalline systems to arbitrary applied electromagnetic fields. The approach leads to the introduction of microscopic polarization and magnetization fields, as well as free charge and current densities, the dynamics of which are described by a lattice gauge theory. The spatial averages of such quantities constitute the fields of macroscopic electrodynamics. We implement this formalism to study the orbital electronic response of a class of insulators to applied uniform dc electric and magnetic fields at zero temperature. To first-order in the applied fields, the free charge and current densities vanish; thus the response of the system is characterized by the first-order modifications to the microscopic polarization and magnetization fields. Associated with the dipole moment of the microscopic polarization (magnetization) field is a macroscopic polarization (magnetization), for which we extract various response tensors. We focus on the orbital magnetoelectric polarizability (OMP) tensor, and find the accepted expression as derived from the "modern theory of polarization and magnetization." Since our results are based on the spatial averages of microscopic fields, we can identify the distinct contributions to the OMP tensor from the perspective of this microscopic theory, and we establish the general framework in which extensions to finite frequency can be made.
Highlights
Interest in describing the response of insulators to external electromagnetic fields dates back to the earliest studies of electricity and magnetism
In pioneering work near the start of the twentieth century, Lorentz [1] based his definition of the macroscopic polarization and magnetization fields on a physical picture of molecules with electric and magnetic moments [2], and from that perspective addressed the response of the macroscopic quantities to the electromagnetic field
In previous work [10], we considered the calculation of the expectation values of the electronic charge and current density operators for a crystalline insulator perturbed by an electromagnetic field
Summary
Interest in describing the response of insulators to external electromagnetic fields dates back to the earliest studies of electricity and magnetism. We present a calculation of the OMP tensor within our framework of identifying microscopic polarization and magnetization fields It is a special case of our general approach, in which by using a set of orthogonal functions that are well-localized spatially one can associate a portion of a total quantity with the point about which each of these functions is localized; a total quantity can be decomposed into “site” contributions. II, we extend the formalism [10] where necessary in order to calculate the modification of a site quantity due to arbitrary electromagnetic fields This is a very general development, and only in the later sections do we restrict ourselves to the limit of uniform and static electric and magnetic fields.
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