Abstract | We propose a theory for how the weak phonon-mediated interaction (JA = 1 ∼ 4meV) wins over the prohibitive Coulomb repulsion (U=30∼60meV) and leads to a nematic superconductor in magic-angle twisted bilayer graphene (MATBG). We find the pairing mechanism akin to that in the A3C60 family of molecular superconductors: Each AA stacking region of MATBG resembles a C60 molecule, in that optical phonons can dynamically lift the degeneracy of the moiré orbitals, in analogy to the dynamical Jahn-Teller effect. Such induced JA has the form of an inter-valley anti-Hund’s coupling and is less suppressed than U by the Kondo screening near a Mott insulator. Additionally, we also considered an intra-orbital Hund’s coupling JH 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 quasi-particles must have a pairing (negative) channel in a doped correlated insulator at  , albeit the bare interaction is positive definite. The proof is non-perturbative and based on exact asymptotic behaviors of the vertex function imposed by Ward identities. Existence of an optimal U for superconductivity is predicted. We also analyzed the pairing symmetry. In a large area of the parameter space of JA, JH, the ground state has 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). A fully gapped s-wave pairing is also possible but spans a smaller phase space in the phase diagram.
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