Substrate screening effects on the quasiparticle band gap and defect charge transition levels in MoS2

Monolayer ${\mathrm{MoS}}_{2}$ has emerged as an interesting material for nanoelectronic and optoelectronic devices. The effect of substrate screening and defects on the electronic structure of ${\mathrm{MoS}}_{2}$ are important considerations in the design of such devices. We find a giant renormalization to the free-standing quasiparticle band gap in the presence of metallic substrates, in agreement with recent scanning tunneling spectroscopy and photoluminescence experiments. Our sulfur vacancy defect calculations using the density functional theory plus GW formalism, reveal two charge transition levels (CTLs) in the pristine band gap of ${\mathrm{MoS}}_{2}$. The $(0/\ensuremath{-}1)$ CTL is significantly renormalized with the choice of substrate, with respect to the pristine valence band maximum (VBM). The $(+1/0)$ level, on the other hand, is pinned 100 meV above the pristine VBM for the different substrates. This opens up a pathway to effectively engineer defect charge transition levels in two-dimensional materials through the choice of substrate.