Topological crystalline insulators with C_{2} rotation anomaly

Abstract

Based on first-principles calculations and a symmetry-based indicator analysis, we find a class of topological crystalline insulators (TCIs) with a C_{2} rotation anomaly in a family of Zintl compounds, including Ba_{3}Cd_{2}As_{4}, Ba_{3}Zn_{2}As_{4}, and Ba_{3}Cd_{2}Sb_{4}. The nontrivial band topology protected by the coexistence of C_{2} rotation symmetry and time-reversal symmetry T leads to two surface Dirac cones at generic momenta on both top and bottom surfaces perpendicular to the rotation axis. In addition, (d−2)-dimensional helical hinge states are also protected along the hinge formed by two side surfaces parallel to the rotation axis. We develop a method based on the nested Wilson loop technique to prove the existence of these surface Dirac cones due to a C_{2} anomaly and precisely locate them as demonstrated in studying these TCIs. The helical hinge states are also calculated. Finally, we show that external strain can be used to tune the topological phase transitions among TCIs, strong Z_{2} topological insulators, and trivial insulators.