Optical signatures of states bound to vacancy defects in monolayer MoS2

The nonzero thickness of single-layer (SL) MoS2 manifests in electron states forming classes of states that are even and odd with respect to reflections through the central plane. These states are energetically well separated: In particular, we show that pristine SL MoS2 exhibits two band gaps, E-g parallel to = 1.9 eV and E-g perpendicular to = 3.2 eV, for the optical in-plane and out-of-plane susceptibilities chi(parallel to) and chi(perpendicular to), respectively. Because of this, odd states are often neglected, which effectively reduces SL MoS2 to a perfect two-dimensional system. We study states bound to defects in SL MoS2 with three types of vacancy defects (VDs), (i) Mo vacancy, (ii) S-2 vacancy, and (iii) 3 x MoS2 quantum antidot, and show that odd states play an equally important role as the even states. In particular, we show that odd states bound to VDs lead to resonances in chi(perpendicular to) inside E-g perpendicular to in SL MoS2 with VDs. Additionally, we demonstrate that the states bound to VDs are not necessarily confined to the band gap in the even subsystem, which necessitates extending the energy region affected by the bound states.