Ab-initio Calculations of Vibrational Fingerprints in the Photoluminescence of Graphene Quantum Dots

We use a computational method based on ab initio (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 find that only few phonon modes couple effectively to the exciton, 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 fingerprint for the determination of size and shape of graphene quantum dots. Our results are in very good agreement with a recent experiment and reveal that a two-phonon replica (with n = 2) is clearly visible in the spectrum.