  We theoretically explore the effect of metal and disulphur vacancies on
electronic and optical properties of MoS$_2$ and WS$_2$ monolayers based on a
Slater-Koster tight-binding model and including the spin-orbit coupling. We
show that the vacancy defects create electronic flat bands by shifting the
Fermi level towards the valence band, indicating that both types of vacancies
may act as acceptor sites. The optical spectra of the pristine monolayers show
step-like features corresponding to the transition from spin split valence band
to the conduction band minimum, whereas the defective monolayers exhibit
additional peaks in their spectra arising from induced midgap states in their
band structures. We find that Mo and W vacancies contribute mostly in the
low-energy optical spectrum, while the S$_2$ vacancies enhance the optical
conductivity mainly in the visible range of the spectrum. This suggests that
depending on the type of vacancy, the atomic defects in MoS$_2$ and WS$_2$
monolayers may increase the efficiency of solar cells used in photovoltaic
systems.
