Doped moir\'e magnets: renormalized flat bands and excitonic phases

We explore the phase diagram of a twisted bilayer of strongly interacting electrons on a honeycomb lattice close to half-filling using the slave boson mean-field theory. Our analysis indicates that a variety of new phases can be realized as a function of chemical doping and twist angle. In particular, we find a non-magnetic excitonic insulating phase that breaks the translational symmetry of the underlying moir\'e pattern. This phase results from the interplay of strong Coulomb interactions and the twist angle. In addition, we show that the features of the renormalized dispersion such as the magic angles depend significantly on the interactions. Our results highlight the rich physics arising in doped moir\'e superlattices of Mott insulators.