<i>Ab initio</i> calculations of vibrational fingerprints in the photoluminescence of graphene quantum dots

We used a computational method based on <i>ab initio</i> (constrained) density functional theory to obtain the photoluminescence spectrum of graphene quantum dots with up to 240 carbon atoms, including the effect of multiphonons. We found that only a few phonon modes couple effectively to the excitons, namely one size- and shape-dependent global mode and two high frequency local modes. The exciton-phonon coupling decreases with increasing size for all structures and has a magnitude in the mid-range, leading to only relatively small multiphonon effects. We suggest that the photoluminescence sidebands can be used as fingerprints for the determination of the size and shape of graphene quantum dots. Our results are in very good agreement with the results from a recent experiment and reveal that a two-phonon replica (with <i>n</i> = 2) is clearly visible in the spectrum.