Topological Crystalline Insulators

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.

Figure 1

(a) Tetragonal lattice with two atoms $A$ and $B$ along the $c$ axis in the unit cell. (b) The Brillouin zone and four high symmetry points.

Figure 2

(a) Bulk band structure of the tight-binding model along high symmetry lines. (b) Surface states with quadratic band touching exist on (001) face. The tight-binding parameters are shown in the text below Eq. (2).