A powerful hybrid FDTD--TDDFT method is used to study the interaction between classical plasmons of a gold bowtie nanoantenna and quantum plasmons of graphene nanoflakes (GNFs) placed in the narrow gap of the nanoantenna. Due to the hot-spot plasmon of the bowtie nanoantenna, the local-field intensity in the gap increases significantly, so that the optical response of the GNF is dramatically enhanced. To study this interaction between classical and quantum plasmons, we decompose this multiscale and multiphysics system into two computational regions, a classical and a quantum one. In the quantum region, the quantum plasmons of the GNF are studied using the TDDFT method, whereas the FDTD method is used to investigate the classical plasmons of the bowtie nanoantenna. Our analysis shows that in this hybrid system the quantum plasmon response of a molecular-scale GNF can be enhanced by more than two orders of magnitude, when the frequencies of the quantum and classical plasmons are the same. This finding can be particularly useful for applications to molecular sensors and quantum optics.
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