Mott insulation and superconductivity in the cluster Hubbard model for magic-angle twisted bilayer graphene

We investigate the strongly correlated electronic system in magic-angle twisted bilayer graphene. Owing to the extended figure of Wannier orbitals, we study the two-orbital cluster Hubbard model with spin-valley fourfold degeneracy, focusing around half filling of valence bands below the neutrality point. The theory shows relatively impotent long-ranged hoppings after renormalization and predicts multiple Mott insulator phases at fractional filling, not only for integer charges per moire site. From second-order perturbation, spin-valley fluctuations give rise to the pairing attraction, exhibiting superconducting domes adjacent to Mott insulator phases. The cluster interaction generates high entanglement among clusters, implying plenty possibilities of nontrivial states.