The quantum anomalous Hall state with a large band gap and a high Chern number is significant for practical applications in spintronics. By performing first-principles calculations, we investigate electronic properties of the fully fluorinated $1T\text{−}{\mathrm{MoSe}}_2$ monolayer. Without considering the spin-orbit coupling, the band structure demonstrates single-spin semimetallic properties and the trigonal warping around $K_{\pm }$ valleys. The introduction of the spin-orbit coupling opens considerable band gaps of 117.2 meV around the two valleys, leading to a nontrivial quantum anomalous Hall state with a Chern number of $\left|C\right|=2$, which provides two chiral dissipationless transport channels from topological edge states and associated quantized anomalous Hall conductivity. In addition, an effective model is constructed to describe the low-energy physics of the monolayer. Our findings in the ${\mathrm{MoSe}}_2{\mathrm{F}}_2$ monolayer shed light on large-gap quantum anomalous Hall states in two-dimensional materials with the chemical functionalization, and provide opportunities to design low-power and noise-tolerant spintronic devices.

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• Quantum anomalous Hall effect
• Transition metal dichalcogenides
• First-principles calculations