Strong electron-phonon coupling, electron-hole asymmetry, and nonadiabaticity 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. Obtained electron-phonon coupling is nearly isotropic and depends very weakly on electronic band and momentum, indicating that electron-phonon coupling prefers single-gap s-wave superconductivity. Relevant phonon energies are much larger than electron energy scale, going far beyond adiabatic limit. Our results provide a fundamental understanding of the electron-phonon interaction in MA-TBG, highlighting that it can contribute to rich physics of the system.