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