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 moir\'{e} optical phonons are singled out which strongly couple to the flat bands. These modes have localized envelopes in the moir\'{e} scale, while in the atomic scale they inherit the monolayer oscillations like the Kekul\'{e} 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 moir\'{e} scale basis. We hope this model will inspire some insights guiding further studies about the superconductivity and other correlated effects in this system.
@article{arxiv.2402.11824,
title = {Moir\'{e} optical phonons dancing with heavy electrons in magic-angle twisted bilayer graphene},
author = {Hao Shi and Wangqian Miao and Xi Dai},
journal= {arXiv preprint arXiv:2402.11824},
year = {2025}
}