Two-dimensional topological crystalline quantum spin Hall effect in transition metal intercalated compounds

While most of the two-dimensional (2D) topological crystalline insulators (TCIs) belong to group IV-VI narrow-band-gap semiconductors in a square lattice, in the present work we predict a TCI family based on transition metal intercalated compounds in a hexagonal lattice. First-principles calculations combined with a substrate-fixed globally optimal structural search technique show that a layer of Os prefers a uniform distribution between two graphene sheets. Band dispersion calculations reveal a Dirac point and a Dirac nodal ring near the Fermi level. The Dirac point is ascribed to the hybridization of e2 and e2∗ orbitals, and the Dirac ring is formed due to dispersion of s and e1∗ orbitals. Upon inclusion of spin-orbit coupling, these Dirac states open topologically nontrivial local band gaps, which are characterized by nonzero mirror Chern numbers. The quantum spin Hall effect is also observed by integrating the spin Berry curvature in the Brillouin zone. In contrast to the 2D group IV-VI TCIs whose band inversions at X and Y points are "locked" by C4 rotation symmetry, here the relative energy of two local band gaps can be manipulated by in-plane biaxial strains. Some other similar intercalation compounds are also shown to be topologically nontrivial. Our work extends the 2D TCI family into a hexagonal lattice composed of transition metals.