Sluggish Valence Fluctuations and Rapid Phonons: Polaronic Coulomb Renormalization and Superconductivity in MATBG

In magic-angle twisted bilayer graphene (MATBG), it was recently highlighted by Lau and Coleman (arXiv:2303.02670) that the optical K-phonons strongly coupled to flat band electrons are faster than the sluggish valence fluctuations of localized states in the topological heavy fermion model, contrasting with heavy fermion compounds where valence fluctuations outpace lattice dynamics. This reversed timescale hierarchy in MATBG introduces the unique possibility of forming polaronic states, potentially explaining Coulomb renormalization effects necessary to bridge the discrepancy between the calculated and measured onsite U and the recently identified phenomenological binding potential required to reproduce the partial chemical potential reset observed around each integer filling factor. We also discuss the role of the attractive optical K-phonon induced intervalley Hund's interaction in superconductivity.