Zero-phonon line emission of single photon emitters in helium-ion treated MoS$_2$

We explore the zero-phonon line of single photon emitters in helium-ion treated monolayer MoS$_2$, which are currently understood in terms of single sulfur-site vacancies. By comparing the linewidths of the zero-phonon line as extracted directly from optical spectra with values inferred from the first-order autocorrelation function of the photoluminescence, we quantify bounds of the homogeneous broadening and of phonon-assisted contributions. The results are discussed in terms of both the independent boson model and ab-initio results as computed from GW and Bethe-Salpeter equation approximations.