Substrate screening effects on the quasiparticle band gap and defect charge transition levels in MoS$_2$

Abstract: Monolayer 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 MoS$_2$ are important considerations in the design of such devices. Here, we present ab initio density functional theory (DFT) and GW calculations to study the effect of substrate screening on the quasiparticle band gap and defect charge transition levels (CTLs) in monolayer MoS$_2$. We find a giant renormalization to the free-standing quasiparticle band gap by 350 meV and 530 meV in the presence of graphene and graphite as substrates, respectively. Our results are corroborated by recent experimental measurements on these systems using scanning tunneling spectroscopy and photoluminescence excitation spectroscopy. Sulfur vacancies are the most abundant native defects found in MoS$_2$. We study the CTLs of these vacancies in MoS$_2$ using the DFT+GW formalism. We find (+1/0) and (0/-1) CTLs appear in the pristine band gap of MoS$_2$. Substrate screening results in renormalization of the (0/-1) level, with respect to the valence band maximum (VBM), by the same amount as the gap. This results in the pinning of the (0/-1) level about $\sim$500 meV below the conduction band minimum for the free-standing case as well as in the presence of substrates. The (+1/0) level, on the other hand, lies less than 100 meV above the VBM for all the cases.