Moiré optical phonons dancing with heavy electrons in magic-angle twisted bilayer graphene

Electron-phonon coupling in magic-angle twisted bilayer graphene is an important but difficult topic. We propose a scheme to simplify and understand this problem. Weighted by the coupling strength with the low-energy heavy electrons (f orbitals), several moiré optical phonons are singled out which strongly couple to the flat bands. These modes have localized envelopes in the moiré scale, while in the atomic scale they inherit the monolayer oscillations like the Kekulé pattern. They flip the flavor of f orbitals, helping stabilize some symmetry-breaking orders. Such electron-phonon couplings are incorporated into an effective extended Holstein model, where both phonons and electrons are written as moiré scale basis. We hope this model will inspire some insights guiding further studies about the superconductivity and other correlated effects in this system.