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 $b_{\mu }$. The value of $b_{\mu }$ 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 $\overrightarrow{b}$ or a domain wall of a component of $\overrightarrow{b}$ can trap surface charges.

• Received 20 August 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.146602