Topological Crystalline Insulators

TL;DR

This paper introduces topological crystalline insulators, a new class of materials with symmetry-protected surface states, expanding the landscape of topological phases beyond traditional topological insulators.

Contribution

It extends the classification of topological insulators to include crystalline symmetries, identifying a new class with unique surface states and Z2 invariants.

Findings

Discovery of topological crystalline insulators with metallic surface states

Surface states exhibit quadratic band degeneracy

Characterization using new Z2 invariants

Abstract

The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point group symmetry of crystals. We find a class of three-dimensional "topological crystalline insulators" which have metallic surface states on certain high symmetry crystal surfaces. These topological crystalline insulators can be viewed as the counterpart of topological insulators in materials without spin-orbit coupling. Their surface states have quadratic band degeneracy instead of linear Dirac dispersion. Their band structures are characterized by new Z2 invariants. We hope this work will enlarge the family of topological phases in band insulators and stimulate the search for them in real materials.