Two-dimensional transition-metal halogenides with Mexican-hat-shaped band as a correlated topological insulator

Graphene, the atomic layer of carbon, is one of the most intensely studied objects since it was isolated for the first time in 2004. However, its Dirac bands are made up of pz orbitals, which creates certain limitations in correlated physics. Here, we replace carbon with transition-metal atoms (M: Ti, Zr, and Hf) to form a corrugated honeycomb lattice. Moreover, both the topside and downside are passivized by halogen atoms (X: F, Cl, Br, and I), making sure that all of them are thermodynamically stable. Due to the irregularly octahedral crystalline field on M-d orbitals, two energy bands derived from dxy and dx2−y2 orbitals intersect each other at the center of the Brillouin zone. Unlike graphene, this intersection is not conical but bell-shaped, further showing the Mexican-hat-shaped dispersion slightly higher than the Fermi level for TiCl, TiBr, and MI (M: Ti, Zr, and Hf). Moreover, the Mexican-hat coefficient could be controllably modulated by the biaxial strain. More interestingly, these intersecting points are robust on the on-site Coulomb interaction, but could be split by the spin-orbital coupling (SOC). Due to the strong SOC strength of correlated dxy and dx2−y2 orbitals, the gap induced by SOC is three orders of magnitude larger than that of pz orbitals in graphene. Furthermore, the topological invariant and edge-states spectrum are calculated to suggest that transition-metal halogenides are non-trivial topological insulators with the topological invariant Z2=1.