Atomistic study of electron-phonon coupling in magic-angle twisted bilayer graphene

We report strong electron-phonon coupling in magic-angle twisted bilayer graphene (MA-TBG) obtained from atomistic description of the system including more than 10,000 atoms in the moiré supercell. Electronic structure, phonon spectrum, and electron-phonon coupling strength λ are obtained before and after atomic-position relaxation both in- and out-of-plane. Obtained λ is very large for MA-TBG, with λ > 1 near the half-filling energies of the flat bands, while it is small (λ~0.1) for monolayer and unrotated bilayer graphene. Significant electron-hole asymmetry occurs in the electronic structure after atomic-structure relaxation, so λ is much stronger with hole doping than electron doping. Electron-phonon coupling is nearly isotropic and very weakly dependent on electron momentum, suggesting single-gap s-wave superconductivity. Relevant phonon energies are much larger than electron energy scale, going far beyond adiabatic limit. Our results provide fundamental understanding of electron-phonon interaction in MA-TBG, highlighting that it can contribute to rich physics of the system.