Phases of a phenomenological model of twisted bilayer graphene

Recent measurements in magic-angle twisted bilayer graphene find a correlated insulator flanked by superconducting domes upon tuning the gate voltage. These results have prompted an analogy with the high-${T}_{c}$ cuprates and the physics of doped Mott insulators. Here, the authors instead propose an analogy with alkali-doped C${}_{60}$ and a violation of Hund's first rule, whereby the resultant attractive interactions, as opposed to a large repulsive Hubbard $U$, are responsible for superconductivity. A two-band phenomenological model for twisted bilayer graphene is studied, which includes nematic orbital ferromagnet and orbital-triplet spin-singlet superconducting broken-symmetry phases.