Optical signatures of states bound to vacancy defects in monolayer MoS₂

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We show that pristine MoS₂ single layer (SL) exhibits two bandgaps Eg∥=1.9 eV and Eg⊥=3.2 eV for the optical in-plane and out-of-plane susceptibilities χ∥ and χ⊥, respectively. In particular, we show that odd states bound to vacancy defects (VDs) lead to resonances in χ⊥ inside Eg⊥ in MoS₂ SL with VDs. We use density functional theory, the tight-binding model, and the Dirac equation to study MoS₂ SL with three types of VDs: (i) Mo-vacancy, (ii) S₂-vacancy, and (iii) 3₂ quantum antidot. The resulting optical spectra identify and characterize the VDs.