Electromagnetic Response of Three-dimensional Topological Crystalline Insulators

TL;DR

This paper investigates the electromagnetic response of 3D topological crystalline insulators with surface Dirac nodes protected by symmetries, revealing how their electromagnetic properties relate to surface states and can trap charges.

Contribution

It introduces a model linking the electromagnetic response to the surface Dirac nodes via a 1-form $b_{}$, providing new insights into charge trapping mechanisms.

Findings

Surface Dirac nodes are characterized by a 1-form $b_{}$.

Vortex cores or domain walls of $b_{}$ can trap surface charges.

Electromagnetic response is coupled to surface states through $b_{}$.

Abstract

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.