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Structural defects can crucially impact the optical response of monolayer(ML) thick materials as they enable trapping sites for excitons. These trappedexcitons appear in photoluminescence spectra as new emissions below the freebright exciton and it can be exploited for single photon emissions (SPE). Inthis work we outline criteria, within our frame work, by which single photonemission can be detected in two dimensional materials and we explore how thesecriteria can be fulfilled in atomically thin transition metal dichalcogenides(TMD). In particular, we model the effect of defects, in accordance with themost common experimental realisations, on the spatial autocorrelation functionof the random disorder potential. Moreover, we provide a way to control theradiative lifetime of these emissions by a hybride heterostructrue of the MLTMD with a graphene sheet and a dielectric spacer that enables the Forsterresonance energy transfer process. Our work predict that the corresponding SPEquenched radiative lifetime will be in the picosecond range, this time scale isin good agreement with the recently measured exciton lifetime in thisheterostructures

Manipulating single photon emitter radiative lifetime in transition-metal dichalcogenides through Forster resonance energy transfer to graphene