Microscopic perspective on the magnetoelectric response of an insulator

We implement a microscopic theory of polarization and magnetization to calculate the magnetoelectric response of an insulator at zero temperature. To first order in the applied fields the free charge and current densities vanish, and as a consequence the response of the system is characterized by the first-order corrections to the microscopic polarization and magnetization fields arising from the applied electric and magnetic fields. Associated with the dipole moment of the microscopic polarization (magnetization) field is a macroscopic polarization (magnetization), for which we extract various response tensors. The magnetoelectric tensor is composed of two distinct parts: the Chern-Simons and cross-gap contributions. We compare our results for these with those of earlier work. We analyze the origin of both the Chern-Simons and cross-gap terms from the perspective of our microscopic theory, and find the former to arise from more “localized” contributions to the response, while the latter to arise from more “extended” contributions.