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, 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, anharmonic effects 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 this mode, 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 the Raman active G mode near the magic angle.