Phonon Linewidths in Twisted Bilayer Graphene near Magic Angle

We present a computational study of the phonon linewidths in twisted bilayer graphene arising from electron-phonon interactions and anharmonic effects. The electronic structure is calculated using distance-dependent transfer integrals based on the atomistic Slater-Koster tight-binding formalism. Furthermore, electron-electron interactions are treated at the Hartree level. The force constants for the phonon calculations are generated from classical force fields. These ingredients are used to calculate the phonon linewidths arising from electron-phonon interactions. Additionally, we account for the effects of phonon-phonon interactions on the linewidths by computing the mode-projected velocity autocorrelation function from classical molecular dynamics. Our findings show that both electron-phonon and anharmonic effects have a significant impact on the linewidth of the Raman active G mode near the magic angle. We predict a moir\'e potential induced splitting of this mode, which arises due to contributions from high symmetry stacking regions.