Electron– K -phonon interaction in twisted bilayer graphene

The authors develop here an analytical theory to describe the interaction between moir\'e electrons and K-phonons, which is responsible for the replica flat bands of twisted bilayer graphene observed in experiments. They perform an exhaustive numerical, analytical, and symmetry-based description of phonon-mediated attractive interaction and superconducting pairing channels from the K-phonon, and find the competing singlet gapped inter-Chern-band channel and nematic gapless intra-Chern-band channel. The latter shows a gapless spectrum with nodes, a feature observed in recent experiments.