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).

Correlated Charge Density Wave Insulators in Chirally Twisted Triple Bilayer Graphene.

Electrons residing in a flat-band system can play a vital role in triggering spectacular phenomenology due to relatively large interactions and spontaneous breaking of different degeneracies. In this work, we demonstrate chirally twisted triple bilayer graphene, a new moiré structure formed by three pieces of helically stacked Bernal bilayer graphene, as a highly tunable flat-band system. In addition to the correlated insulators showing at integer moiré fillings, commonly attributed to interaction induced symmetry broken isospin flavors in graphene, we observe abundant insulating states at half-integer moiré fillings, suggesting a longer-range interaction and the formation of charge density wave insulators which spontaneously break the moiré translation symmetry. With weak out-of-plane magnetic field applied, as observed half-integer filling states are enhanced and more quarter-integer filling states appear, pointing toward further quadrupling moiré unit cells. The insulating states at fractional fillings combined with Hartree-Fock calculations demonstrate the observation of a new type of correlated charge density wave insulators in graphene and points to a new accessible twist manner engineering correlated moiré electronics.