Model for the metal-insulator transition in graphene superlattices and beyond

In bilayer graphene with a small twist angle, the moir\'e pattern creates a superlattice with over 10000 atoms per supercell and complex minibands with a small bandwidth. The low-energy narrow bands host correlated insulating and unconventional superconducting phases discovered recently. Here, the authors introduce a two-orbital tight-binding and Hubbard model on a honeycomb lattice to capture the physics of these narrow bands. This model provides a starting point for studying the metal-insulator transition, Landau level degeneracy lifting, and superconductivity in twisted bilayer graphene.