Molecular Pairing in Twisted Bilayer Graphene Superconductivity

Abstract

We propose a theory for how the weak phonon-mediated interaction ($J_{\mathrm{A}}=1\sim 4$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 $J_{\mathrm{A}}$ 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 $J_{\mathrm{H}}$ 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 $\nu =\pm (2+\delta \nu )$, 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 $J_{\mathrm{A}}$, $J_{\mathrm{H}}$, 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).

References in corpus (5)

• Modeling the Unconventional Superconducting Properties of Expanded A${}_3$C${}_{60}$ Fullerides
• Interplay of Coulomb and electron-phonon interactions in graphene
• Band structure and insulating states driven by the Coulomb interaction in twisted bilayer graphene
• Competing phases of interacting electrons on triangular lattices in moiré heterostructures
• Dynamical correlations and order in magic-angle twisted bilayer graphene

Cited by in corpus (10)

• Theory of Topological Superconductivity and Antiferromagnetic Correlated Insulators in Twisted Bilayer WSe${}_2$
• Moiré optical phonons dancing with heavy electrons in magic-angle twisted bilayer graphene
• Electron phonon coupling in the topological heavy fermion model of twisted bilayer graphene
• Nodal Nematic Superconductivity in Multiple-Flat-Band Land
• Bypassing the lattice BCS-BEC crossover in strongly correlated superconductors: resilient coherence from multiorbital physics
• Nonflat bands and chiral symmetry in magic-angle twisted bilayer graphene
• Oscillate and Renormalize: Fast Phonons Reshape the Kondo Effect in Flat Band Systems
• Momentum-resolved spectroscopy of superconductivity with the quantum twisting microscope
• Flat-band projected versus fully atomistic twisted bilayer graphene
• Microscopic theory for electron-phonon coupling in twisted bilayer graphene