First-principles identification of topological crystalline insulators with C2 rotation anomaly

Recently, the concept of a rotation anomaly in the surface of ${C}_n$ rotation ($n=2,4,6$) protected topological crystalline insulators (TCIs) was proposed. However, verified material realizations of the rotation anomaly are still rare. Furthermore, owing to fruitful crystallographic symmetries, in addition to the rotation protected surface states, other kinds of topological boundary states could also emerge on suitable surfaces or hinges in one material, which is promising for manipulation in device applications. In this work, we identify a ${C}₂$ rotation anomaly in 24 TCIs and furthermore ascertain the positions of coexisting topological boundary states by first-principles calculations. Of these TCIs, using BiSe in space group 164 to illustrate, we demonstrate the mirror and ${C}₂$ rotation protected surface states in specific surfaces as well as the ${C}₂$ protected hinge states between two side surfaces. The predicated TCI materials with the ${C}₂$ rotation anomaly have diverse structures and chemical compositions and thus provide a good reference for future experimental studies.