Optical activity of a bulk Chern insulator

We describe the optical response of a bulk Chern insulator in three dimensions, using a formalism based on microscopic polarization and magnetization fields in extended media. The induced macroscopic current density is related to this applied field through a conductivity tensor that is a sum of two terms, one of which is a frequency-dependent contribution that describes the analogue for a Chern insulator of the usual Kubo response in a topologically trivial insulator, while the other describes the quantum anomalous Hall effect in a generic three-dimensional crystal lattice. In the absence of time-reversal symmetry, the off-diagonal parts of both terms lead to a rotation of the plane of polarization of an incident field, describing the optical activity of a bulk Chern insulator. We summarize the results of this calculation.