Electromagnetic Response of Three-Dimensional Topological Crystalline Insulators

Topological crystalline insulators are a new class of materials that have metallic surface states on select surfaces due to point group crystalline symmetries. In this Letter, we consider a model for a three-dimensional topological crystalline insulator with Dirac nodes occurring on a surface that are protected by the mirror symmetry. We demonstrate that the electromagnetic response for such a system is characterized by a 1-form b_{μ}. The value of b_{μ} can be inferred from the locations of the surface Dirac nodes in energy-momentum space. From both the effective action and analytical band structure calculations, we show that the vortex core of b[over →] or a domain wall of a component of b[over →] can trap surface charges.