Theories for the correlated insulating states and quantum anomalous Hall effect phenomena in twisted bilayer graphene

Based on an all-band moir\'e Hartree-Fock variational method, the authors study theoretically the correlated and topological states in magic-angle twisted bilayer graphene. They construct phase diagrams at various integer fillings. In particular, a so far unknown quantum state of matter, the moir\'e orbital antiferromagnetic state, is identified as the possible ground state at some fillings.