Topological crystalline insulators (TCIs) are insulating electronic phases of matter with nontrivial topology originating from crystalline symmetries. Recent theoretical advances have proposed new TCI states protected by rotational symmetries and provided powerful guidelines to search for TCIs in real materials. Building upon recent theoretical works, we demonstrate a feasible method to identify new TCI states based on first-principles calculations. We systematically unveil the topological properties of the TCI states in ${\mathrm{Ca}}_2\mathrm{As}$. On both top and side surfaces, we observe topological surface states protected independently by rotational and mirror symmetries. We show that a particular lattice distortion can single out the newly proposed topological protection by the rotational symmetry. As a result, the Dirac points of the topological surface states are moved to generic locations in momentum space away from any high-symmetry lines. Such topological surface states have not been seen before. Moreover, the other family members, including ${\mathrm{Ca}}_2\mathrm{Sb}$, ${\mathrm{Ca}}_2\mathrm{Bi}$, and ${\mathrm{Sr}}_2\mathrm{Sb}$, feature different topological surface states due to their distinct topological invariants. We thus further propose topological phase transitions in the pseudobinary systems such as ${\left({\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\right)}_2\mathrm{As}$ and ${\mathrm{Ca}}_2{\mathrm{As}}_x{\mathrm{Sb}}_{1-x}$. Our work reveals rich and exotic TCI physics across the ${\mathrm{Ca}}_2\mathrm{As}$ family of materials and demonstrates a complete roadmap for uncovering TCIs topological nature based on first-principles calculations. Such a method can be broadly applied in searching for new TCIs.

• Received 14 May 2018

DOI:https://doi.org/10.1103/PhysRevB.98.241104