Engineering topological states in a two-dimensional honeycomb lattice.

In this work, we use first-principles calculations to determine the interplay between spin-orbit coupling (SOC) and magnetism which can not only generate a quantum anomalous Hall state but can also result in topologically trivial states although some honeycomb systems host large band gaps. By employing tight-binding model analysis, we have summarized two types of topologically trivial states: one is due to the coexistence of quadratic non-Dirac and linear Dirac bands in the same spin channel that act together destructively in magnetic materials (such as, CrBr, CrCl, and VBr monolayers); the other one is caused by the destructive coupling effect between two different spin channels due to small magnetic spin splitting in heavy-metal-based materials, such as, BaTe(111)-supported plumbene. Further investigations reveal that topologically nontrivial states can be realized by removing the Dirac band dispersion of the magnetic monolayers for the former case (such as in alkali metal doped CrBr), while separating the two different spin channels from each other by enhancing the magnetic spin splitting for the latter case (such as in half-iodinated silicene). Thus, our work provides a theoretical guideline to manipulate the topological states in a two-dimensional honeycomb lattice.