Surface states in Dirac metals and topological crystalline insulators

TL;DR

This paper investigates the surface states in Dirac metals and topological crystalline insulators, revealing how symmetry breaking affects their topological properties and surface spectra, and identifying phase transitions characterized by mirror Chern numbers.

Contribution

It demonstrates that surface states in Dirac metals form branches ending at Dirac points and explores how breaking rotational symmetry leads to topological crystalline insulator phases with mirror symmetry protection.

Findings

Surface states in Dirac metals always form branches terminating at Dirac points.

Breaking rotational symmetry gaps Dirac points, leading to topological crystalline insulator phases.

Mirror symmetry protects certain surface states, resulting in phases with one or three Dirac points.

Abstract

We reconsider the problem of surface states spectrum in type One Dirac metals. We find that the surface states, despite being gapped, always form branches terminating at Dirac points. Furthermore, we consider evolution of the surface states in the case, when rotational symmetry is broken, and as a result, Dirac points are gapped. We find, that in this case, special role is played by mirror symmetry relative to the plane connecting Dirac points. When it is present, the resulting gapped state is a topological crystalline insulator, which surface spectrum can contain either one or three Dirac points, two of which are protected solely by the mirror symmetry. Thus, the Dirac metal can be viewed as a topological phase transition between two phases with different mirror Chern numbers.