Molecular Pairing in Twisted Bilayer Graphene Superconductivity.

We propose a theory for how the weak phonon-mediated interaction (J_{A}=1-4 meV) wins over the prohibitive Coulomb repulsion (U=30-60 meV) and leads to a superconductor in magic-angle twisted bilayer graphene (MATBG). We find the pairing mechanism akin to that in the A_{3}C_{60} family of molecular superconductors: Each AA stacking region of MATBG resembles a C_{60} molecule, in that optical phonons can dynamically lift the degeneracy of the moiré orbitals, in analogy to the dynamical Jahn-Teller effect. Such induced J_{A} has the form of an intervalley anti-Hund's coupling and is less suppressed than U by the Kondo screening near a Mott insulator. Additionally, we also considered an intraorbital Hund's coupling J_{H} that originates from the on-site repulsion of a carbon atom. Under a reasonable approximation of the realistic model, we prove that the renormalized local interaction between quasiparticles has a pairing (negative) channel in a doped correlated insulator at ν=±(2+δν), albeit the bare interaction is positive definite. The proof is nonperturbative and based on exact asymptotic behaviors of the vertex function imposed by Ward identities. Existence of an optimal U for superconductivity is predicted. In a large area of the parameter space of J_{A}, J_{H}, the ground state is found to have a nematic d-wave singlet pairing, which, however, can lead to a p-wave-like nodal structure due to the Berry's phase on Fermi surfaces (or Euler obstruction).