  The deterministic production of single-photons from two dimensional materials
promises to usher in a new generation of photonic quantum devices. In this
work, we outline criteria by which single-photon emission can be realised in
two dimensional materials: spatial isolation, spectral filtering and low
excitation of quantum emitters. We explore how these criteria can be fulfilled
in atomically thin transition metal dichalcogenides, where excitonic physics
dictates the observed photoemission. In particular, we model the effect of
defects and localised strain, in accordance with the most common experimental
realisations, on the photon statistics of emitted light. Moreover, we
demonstrate that an optical cavity has a negative impact on the photon
statistics, suppressing the single-photon character of the emission by
diminishing the effect of spectral filtering on the emitted light. Our work
provides a theoretical framework revealing criteria necessary to facilitate
single-photon emission in two-dimensional materials and thus can guide future
experimental studies in this field.
