  Associating the presence of atomic vacancies to excited-state transport
phenomena in two dimensional semiconductors is of emerging interest, and
demands detailed understanding of the involved exciton transitions. Here we
study the effect of such defects on the electronic and optical properties of
WS$_2$-graphene and MoS$_2$-graphene van der Waals heterobilayers by employing
many-body perturbation theory. We find that the combination of chalcogen
defects and graphene adsorption onto the transition metal dichalcogenide layer
can radically alter the optical properties of the heterobilayer, due to a
combination of dielectric screening, the impact of the missing chalcogen atoms
in the intralayer and interlayer optical transitions, and the different nature
of each layer. By analyzing the intrinsic radiative rates of the most stable
subgap excitonic features, we find that while the presence of defects
introduces low-lying optical transitions, resulting in excitons with larger
oscillator strength, it also decreases the optical response associated to the
pristine-like transition-metal dichalcogenide intralayer excitons. Our findings
relate excitonic features with interface design for defect engineering in
photovoltaic and transport applications.
