Topological Crystalline Insulators

TLDR

The recent discovery of topological insulators has revived interest in the band topology of insulators. The study extends the topological classification of band structures to include certain crystal point group symmetries. This extension is achieved by incorporating crystal point group symmetry into the classification framework. The authors identify a class of three‑dimensional topological crystalline insulators with metallic surface states exhibiting quadratic band degeneracy on high‑symmetry crystal surfaces, characterized by new topological invariants, and propose that these materials, which lack spin‑orbit coupling, broaden the family of topological phases and encourage experimental searches.

Abstract

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