Quadratic band crossing induced quantum anomalous Hall effect in monolayer MoT e 2 F 2

The quantum anomalous Hall effect (QAHE) has gained significant attention in recent years due to its potential applications in low-power devices. However, the QAHE still faces the limitations of the relatively small global band gap and low Chern number. In this work, based on the tight-binding (TB) model with magnetic group $P\overline{3}{m}^{\ensuremath{'}}1$, we propose a mechanism whereby quadratic band crossing induces a stable global band gap which is larger than that formed by the linear band crossing. Additionally, the quadratic band crossing induces topological states with high Chern number when spin-orbit coupling is considered. We also propose monolayer $\mathrm{MoT}{\mathrm{e}}₂{\mathrm{F}}₂$ to confirm the TB results by performing calculations of first-principles and low-energy $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ model. The quadratic band crossing is formed by the hybridization of the orbitals from the Mo and the F atoms. The contributions of the ${d}_xy$ and ${d}_{{x}²\ensuremath{-}{y}²}$ orbitals at the quadratic band crossing are bigger than their contributions at the linear band crossing, so the global band gap induced by the quadratic band crossing is large. Furthermore, after biaxial strains are applied, the quadratic band crossing is destroyed and it transfers into a linear band crossing, and the global band gap becomes small. The quadratic band crossing can also be manipulated by a vertical electric field, and a phase transition from the QAHE to the anomalous valley Hall effect can be achieved. Our work not only provides a method to discover two-dimensional materials with a large global band gap and high Chern number but also integrates topological electronics and valleytronics, promoting the development of low-power devices.