  The near-field Coulomb interaction between a nano-emitter and a graphene
monolayer results in strong F\"orster-type resonant energy transfer and
subsequent fluorescence quenching. Here, we investigate the distance dependence
of the energy transfer rate from individual, i) zero-dimensional CdSe/CdS
nanocrystals and ii) two-dimensional CdSe/CdS/ZnS nanoplatelets to a graphene
monolayer. For increasing distances $d$, the energy transfer rate from
individual nanocrystals to graphene decays as $1/d^4$. In contrast, the
distance dependence of the energy transfer rate from a two-dimensional
nanoplatelet to graphene deviates from a simple power law, but is well
described by a theoretical model, which considers a thermal distribution of
free excitons in a two-dimensional quantum well. Our results show that accurate
distance measurements can be performed at the single particle level using
graphene-based molecular rulers and that energy transfer allows probing
dimensionality effects at the nanoscale.
