Berry-phase description of Topological Crystalline Insulators

Understand

We study a class of translational-invariant insulators with discrete rotational symmetry.

• These insulators have no spin-orbit coupling, and in some cases have no time-reversal symmetry as well, i.e., the relevant symmetries are purely crystalline.
• Nevertheless, topological phases exist which are distinguished by their robust surface modes.
• Like many well-known topological phases, their band topology is unveiled by the crystalline analog of Berry phases, i.e., parallel transport across certain non-contractible loops in the Brillouin zone.