Topological Dirac states in transition-metal monolayers on graphyne

Realizing topological Dirac states in two-dimensional (2D) magnetic materials is particularly important to spintronics. Here, we propose that such states can be obtained in a transition-metal (Hf) monolayer grown on a 2D substrate with hexagonal hollow geometry (graphyne). We find that the significant orbital hybridizations between Hf and C atoms can induce sizable magnetism and bring three Dirac cones at/around each high-symmetry K(K′) point in the Brillouin zone. One Dirac cone is formed by pure spin-up electrons from the dz2 orbital of Hf, and the remaining two are formed by crossover between spin-up electrons from the dz2 orbital and spin-down electrons from the hybridization of the dxy/x²-y2 orbitals of Hf atoms and the p_z orbital of C atoms. We also find that the spin-orbit coupling effect can open sizable band gaps for the Dirac cones. The Berry curvature calculations further show the nontrivial topological nature of the system with a negative Chern number C = -3, which is mainly attributed to the Dirac states. Molecular dynamics simulations confirm the system's thermodynamic stability approaching room temperature. The results provide a new avenue for realizing the high-temperature quantum anomalous Hall effect based on 2D transition-metals.