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Coexistence of intrinsic ferrovalley (FV) and nontrivial band topologyattracts intensive interest both for its fundamental physics and for itspotential applications, namely valley-polarized quantum anomalous Hallinsulator (VQAHI). Here, based on first-principles calculations by usinggeneralized gradient approximation plus $U$ (GGA+$U$) approach, the VQAHIinduced by electronic correlation or strain can occur in monolayer$\mathrm{RuBr_2}$. For perpendicular magnetic anisotropy (PMA), the ferrovalley(FV) to half-valley-metal (HVM) to quantum anomalous Hall (QAH) to HVM to FVtransitions can be driven by increasing electron correlation $U$. However,there are no special QAH states and valley polarization for in-plane magneticanisotropy. By calculating actual magnetic anisotropy energy (MAE), the VQAHIindeed can exist between two HVM states due to PMA, a unit Chern number/achiral edge state and spontaneous valley polarization. The increasing $U$ caninduce VQAHI, which can be explained by sign-reversible Berry curvature or bandinversion between $d_{xy}$/$d_{x^2-y^2}$ and $d_{z^2}$ orbitals. Even thoughthe real $U$ falls outside the range, the VQAHI can be achieved by strain.Taking $U$$=$2.25 eV as a concrete case, the monolayer $\mathrm{RuBr_2}$ canchange from a common ferromagentic (FM) semiconductor to VQAHI under about0.985 compressive strain. It is noted that the edge states of VQAHI arechiral-spin-valley locking, which can achieve complete spin and valleypolarizations for low-dissipation electronics devices. Both energy band gap andvalley splitting of VQAHI in monolayer $\mathrm{RuBr_2}$ are higher than thethermal energy of room temperature (25 meV), which is key at room temperaturefor device applications.

Valley-polarized quantum anomalous Hall insulator in monolayer $\mathrm{RuBr_2}$