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 moire 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 nu = +/-(2+delta nu), 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 p-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).