Phonon linewidths in twisted bilayer graphene near the magic angle

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