Defect states in monolayer transition metal dichalcogenides

Monolayer transition metal dichalcogenides (TMDC) have attracted considerable attention in the past few years. They are direct bandgap semiconductors, with the conduction and valence band edges at the doubly degenerate corners ($\pm$ K points) of the hexagonal Brillouin zone. Recently, by using novel etching techniques, it was possible to remove a controlled number of atoms from monolayer MoS$_{2}$, thereby creating a hexagonally shaped pit. By solving the Dirac equation analytically, we show that a pit gives rise to bound states with interesting properties. In particular, the optical selection rules turn out to be very strict. We confirm our analytical results by means of numerical density functional theory (DFT) calculations.