Moiré flat Chern bands and correlated quantum anomalous Hall states generated by spin-orbit couplings in twisted homobilayer MoS_{2}

We predict that in a twisted homobilayer of transition-metal dichalcogenide MoS_{2}, spin-orbit coupling in the conduction band states from ±K valleys, can give rise to moiré 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.