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Topological crystalline insulators (TCI) are insulating electronic phases ofmatter with nontrivial topology originating from crystalline symmetries. Recenttheoretical advances have provided powerful guidelines to search for TCIs inreal materials. Using density functional theory, we identify a class of new TCIstates in the tetragonal lattice of the Ca$_2$As material family. On both topand side surfaces, we observe topological surface states protectedindependently by rotational and mirror symmetries. We show that a particularlattice distortion can single out the newly proposed topological protection bythe rotational symmetry. As a result, the Dirac points of the topologicalsurface states are moved to generic locations in momentum space away from anyhigh symmetry lines. Such topological surface states have not been seen before.Moreover, the other family members, including Ca$_2$Sb, Ca$_2$Bi and Sr$_2$Sb,feature different topological surface states due to their distinct topologicalinvariants. We thus further propose topological phase transitions in thepseudo-binary systems such as (Ca$_{1-x}$Sr$_x$)$_2$As andCa$_2$As$_x$Sb$_{1-x}$. Our work reveals rich and exotic TCI physics across theCa$_2$As family of materials, and suggests the feasibility of materialsdatabase search methods to discover new TCIs.

Topological crystalline insulator states in the Ca$_2$As family