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In this work, we present a systematic study of the plasmon modes in a systemof vertically stacked pair of graphene discs. Quasistatic approximation is usedto model the eigenmodes of the system. Eigen-response theory is employed toexplain the spatial dependence of the coupling between the plasmon modes and aquantum emitter. These results show a good match between the semi-analyticalcalculation and full-wave simulations. Secondly, we have shown that it ispossible to engineer the decay rates of a quantum emitter placed inside andnear this cavity, using Fermi level tuning, via gate voltages and variation ofemitter location and polarization. We highlighted that by coupling to thebright plasmon mode, the radiative efficiency of the emitter can be enhancedcompared to the single graphene disc case, whereas the dark plasmon modesuppresses the radiative efficiency.

Photon Emission Rate Engineering using Graphene Nanodisc Cavities