Recent experimental results have demonstrated the ability of monolayer MoS2 to efficiently generate second harmonic fields with susceptibilities between 0.1 and 100 nm/V. However, no theoretical calculations exist with which to interpret these findings. In particular, it is of interest to theoretically estimate the modulus of the second harmonic response, since experimental reports on this differ by almost three orders of magnitude. Here, we present single-particle calculations of the second harmonic response based on a tight-binding band structure. We compare directly with recent experimental findings and include in the discussion also spectral features and the effects of multiple layers.The prediction and observation of a direct band gap in monolayer (ML) MoS 2 has revitalized the interest in the optical properties of this material 1-9 . Indeed, a substantial photoluminescence for 1H-MoS 2 has been observed 2,3 . Additionally, several papers 4-6 have recently demonstrated how second harmonic generation (SHG) microscopy can be used to extract important information regarding e.g. the number of layers and crystallographic orientation of few-layered MoS 2 platelets. Furthermore, exfoliated MoS 2 was shown experimentally to display a remarkably large second harmonic signal, with second harmonic susceptibilities on the order of ∼ 100 nm/V reported in Ref. 4 while Refs. 5 and 6 report only ∼ 0.1 nm/V (assuming a homogeneous susceptibility inside the monolayer of thickness ∼ 3Å when relating to sheet second harmonic susceptibilities). Regions covered with an odd number of 2H stacked layers were found to generate second harmonic fields with efficiencies decreasing slightly with the number of layers, while regions with an even number of layers displayed almost vanishing second harmonic signals as expected due to centro-symmetry. 4-6However, few-layered MoS 2 grown by chemical vapour deposition does not follow this trend 4 , possibly due the stacking order of CVD grown films deviating from 2H. In Ref. 5, second harmonic spectra of both ML and trilayer (TL) MoS 2 were presented, demonstrating an intense peak in the second harmonic spectrum at pump photon energies near 1.45 eV, with a slight redshift for TLs compared to MLs.There exists no theoretical work, with which to interpret the experimental findings mentioned above. Hence, in this letter we consider the microscopic origins of the second harmonic response of few-layered MoS 2 based on a tight-binding sp 3 d 5 band structure recently published 10 . At present, it is very computationally demanding to retain the k-space resolution needed to resolve delicate spectral features in a full exciton Bethe-Salpeter calculation. Moreover, the single particle results remain an important first step in the theoretical understanding of the nonlinear optical properties of MoS 2 . We have therefore chosen to omit excitonic effects in the present work and employ the single-particle second harmonic response formalism developed by Moss and Sipe 11,12 . We verify that the experimental me...

Dielectric screening of excitons in 2D semiconductors is known to be a highly non-local effect, which in reciprocal space translates to a strong dependence on momentum transfer q. We present an analytical model dielectric function, including the full non-linear q-dependency, which may be used as an alternative to more numerically taxing ab initio screening functions. By verifying the good agreement between excitonic optical properties calculated using our model dielectric function, and those derived from ab initio methods, we demonstrate the versatility of this approach. Our test systems include: Monolayer hBN, monolayer MoS2, and the surface exciton of a 2 × 1 reconstructed Si(111) surface. Additionally, using our model, we easily take substrate screening effects into account. Hence, we include also a systematic study of the effects of substrate media on the excitonic optical properties of MoS2 and hBN.