Abstract
We predict that in a twisted homobilayer of transition-metal dichalcogenide MoS₂, spin-orbit coupling in the conduction band states from ± K valleys can give rise to moir\'{e} flat bands with nonzero Chern numbers in each valley. The nontrivial band topology originates from a unique combination of angular twist and local mirror symmetry breaking in each individual layer, which results in unusual skyrmionic spin textures in momentum space with skyrmion number S = ± 2. Our Hartree-Fock analysis further suggests that density-density interactions generically drive the system at 1/2-filling into a valley-polarized state, which realizes a correlated quantum anomalous Hall state with Chern number C = ± 2. Effects of displacement fields are discussed with comparison to nontrivial topology from layer-pseudospin magnetic fields.