Molecular Pairing in Twisted Bilayer Graphene Superconductivity

Yi-Jie Wang; Geng-Dong Zhou; Shi-Yu Peng; Biao Lian; Zhi-Da Song

doi:10.1103/PhysRevLett.133.146001

paper

Molecular Pairing in Twisted Bilayer Graphene Superconductivity

arXiv:2402.00869 · doi:10.1103/PhysRevLett.133.146001

Abstract

We propose a theory for how the weak phonon-mediated interaction ( $J_{A} = 1 \sim 4$ meV) wins over the prohibitive Coulomb repulsion ( $U = 30 \sim 60$ 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 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 $J_{H}$ 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 quasi-particles must have a pairing (negative) channel in a doped correlated insulator at $ν = \pm (2 + δ ν)$ , 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 $J_{A}$ , $J_{H}$ , 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).

Molecular Pairing in Twisted Bilayer Graphene Superconductivity

Abstract

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