Theory of Bound Impurity States in Monolayer Transition-Metal Dichalcogenides

Semiconducting monolayer transition-metal dichalcogenides (TMDCs) are two-dimensional (2D) materials that exhibit direct band gaps, favourable for nanoelectronic applications such as field-effect transistors. We discuss the behaviour of single-particle bound states in molybdenum disulphide (MoS₂) with a charged impurity atom adsorbed to its surface. The bound states associated with shallow defect potentials extend over tens of nanometers or more because of weak screening in 2D materials. These long-range screened potentials are difficult to fully capture with conventional DFT supercells. To understand the behaviour of TMDCs with impurities, we employ tight-binding models for systems with 10³-10⁴ atoms, including the static screening of impurity charges through the random phase approximation. We have studied spatial densities of bound impurity states and the local density of states near impurity ions. We find localized Rydberg states near the band edges, with a significant asymmetry between donor and acceptor states, which is related to specific features of the MoS₂ band structure. We also predict signatures of these defect states that can be measured in scanning tunnelling experiments.