Linear response of crystals to electromagnetic fields: Microscopic charge-current density, polarization, and magnetization

摘要

We present an electrodynamic approach to the description of the linear response of solids to electromagnetic fields. For time and spatially varying applied fields we solve the dynamical equations satisfied by the gauge-invariant Green function and find microscopic charge and current densities that result in a form allowing for an easy construction of the multipole expansion of applied fields. Restricting ourselves to static and uniform electric and magnetic fields, we construct microscopic expressions for polarization and magnetization fields associated with each lattice site. The approach is in the spirit of the Power-Zienau-Wooley (PZW) treatment but generalized to account for the motion of the charge between lattice sites. We show that the macroscopic polarization and magnetization can be understood as the spatial average of the generalized PZW microscopic fields.