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The band-edge excitonic properties of AlN are investigated using low-temperature ͑1.7 K͒ optical reflectance and transmission measurements of samples with various crystal orientations. The A, B, and C excitons are found to have energies of 6.025, 6.243, and 6.257 eV in unstrained material, which shift with strain. The results are compared to a calculation of exciton energies and oscillator strengths to yield a crystal-field splitting of −230 meV in unstrained AlN, in good agreement with previous ab initio calculations.

A detailed first-principle study has been performed to evaluate the electronic and optical properties of single-layer (SL) transition metal dichalcogenides (TMDCs) (MX2; M= transition metal such as Mo, W and X= S, Se, Te), in the presence of vacancy defects (VDs). Defects usually play an important role in tailoring electronic, optical, and magnetic properties of semiconductors. We consider three types of VDs in SL TMDCs i) X-vacancy, X2-vacancy, and iii) M -vacancy. We show that VDs lead to localized defect states (LDS) in the band structure, which in turn give rise to sharp transitions in in-plane and out-of-plane optical susceptibilities, χ and χ ⊥ . The effects of spin orbit coupling (SOC) are also considered. We find that SOC splitting in LDS is directly related to the atomic number of the transition metal atoms. Apart from electronic and optical properties we also find magnetic signatures (local magnetic moment of ∼ µB) in MoSe2 in the presence of Mo vacancy, which breaks the time reversal symmetry and therefore lifts the Kramers degeneracy. We show that a simple qualitative tight binding model (TBM), involving only the hopping between atoms surrounding the vacancy with an on-site SOC term, is sufficient to capture the essential features of LDS. In addition, the existence of the LDS can be understood from the solution of the 2D Dirac Hamiltonian by employing infinite mass boundary conditions. In order to provide a clear description of the optical absorption spectra, we use group theory to derive the optical selection rules between LDS for both χ and χ ⊥ . arXiv:1704.02023v1 [cond-mat.mes-hall]

Non-zero thickness of MoS2 single layer (SL) manifests in electron states forming classes of states even and odd with respect to reflections through the central plane. These states are energetically well separated: in particular, we show that pristine MoS2 SL exhibits two bandgaps E g = 1.9 eV and E g⊥ = 3.2 eV for the optical in-plane and out-of-plane susceptibilities χ and χ ⊥ , respectively. Because of this, odd states are often neglected, which effectively reduces MoS2 SL to a perfect 2D system. We study states bound to defects in MoS2 SL with three types of vacancy defects (VD): (i) Mo-vacancy, (ii) S2-vacancy, and (iii) 3×MoS2 quantum antidot -and show that odd states play equally important role as even. In particular, we show that odd states bound to VD lead to resonances in χ ⊥ inside E g⊥ in MoS2 SL with VDs. Additionally, we demonstrate that the states bound to VDs are not necessarily confined to the bandgap in the even subsystem, which necessitates extending the energy region affected by the bound states. 1-7 In order to increase their performance, it is crucial to characterize the defects present in TMDC SLs.Here we show that the bandgap E g⊥ = 3.2 eV for the optical out-of-plane susceptibility χ ⊥ in pristine MoS 2 SL provides a large energy window to characterize vacancy defects (VDs). Pristine MoS 2 SL is invariant with respect to σ h reflection about the z = 0 (Mo) plane, where the z axis is oriented perpendicular to the Mo plane. Therefore, electron states break down into two classes: even and odd, or symmetric and anti-symmetric with respect to σ h . We show below that this leads to the nontrivial consequence that χ z = χ ⊥ has a bandgap of E g⊥ = 3.2 eV, which is substantially larger than the bandgap E g = 1.9 eV for the in-plane component of the optical susceptibility χ x = χ y = χ . As we show, due to the optical selection rules for the even and odd states, there are no π transitions, driven by z-polarized photons, below 3.2 eV. Hence, χ ⊥ for pristine MoS 2 SL must vanish for energies below 3.2 eV. While the even states enjoyed the most attention, 4,6-8 here we show that the odd states need to be considered on equal footing with the even states.Several studies on VDs in 2D materials have emerged recently. The minibands resulting from quantum antidot (QAD) superlattices can be used to tune the bandgaps of graphene 9 and MoS 2 SL 10,11 . Substitutional oxygen defects lead to suppression of conductivity 12 and photoluminescence 13 . VDs in MoS 2 SL have been characterized theoretically in terms of magnetic properties.