Electromagnetic Response of Three-dimensional Topological Crystalline Insulators

Topological crystalline insulators (TCI) are a new class of materials which have metallic surface states on select surfaces due to point group crystalline symmetries. In this letter, we consider a model for a three-dimensional (3D) topological crystalline insulator with Dirac nodes occurring on a surface that are protected by the mirror and time reversal symmetry. We demonstrate that the electromagnetic response for such a system is characterized by a $1$-form $b_{\mu}$. $b_{\mu}$ can be inferred from the locations of the surface Dirac nodes in energy-momentum space and couples to the surface Dirac nodes like a valley gauge field. From both the effective action and analytical band structure calculations, we show that the vortex core of $\vec b$ or a domain wall of a component of $\vec b$ can trap surface charges.