Strong optical nonlinearity of CVD-grown ${\mathrm{MoS}}_2$ monolayer as probed by wavelength-dependent second-harmonic generation

While noncentrosymmetric ${\mathrm{MoS}}_2$ monolayer is known to exhibit efficient second-harmonic generation (SHG), there is currently no agreement on its absolute nonlinear susceptibility ${\chi }^{\left(2\right)}$, varying over three orders of magnitude according to recent experiments. In order to resolve this conflicting issue, we have studied the nonlinear optical properties of ${\mathrm{MoS}}_2$ monolayer grown by chemical vapor deposition. The polycrystalline nature of the monolayer was directly probed by the SHG polarization dependence across the grain boundaries using femtosecond pulses. Broadband wavelength-dependent SHG response $\left(\lambda =1.1–2.0\mu \mathrm{m}\right)$ using picosecond pulses was studied by comparing the relative SHG counts of ${\mathrm{MoS}}_2$ to quartz and incorporating the structural and optical characteristics of the monolayer. Significant nonlinear optical dispersion gives rise to ${\chi }^{\left(2\right)}\sim 430$ pm/V at 580 nm, where SHG is neither affected by any excitonic absorption/resonance nor by fundamental absorption. We also show that ${\chi }^{\left(2\right)}$ must be derived from a thin bulk (sheet) optical nonlinearity and that the previous measurements are in fact all consistent, together with our measurements and first-principle calculations.

Figure 1

(a) Schematic of ${\mathrm{MoS}}_2$ crystal structure (mirror axis shown in blue) viewed along the $c$ axis and (b) its band structure calculated using LDA. (c) SEM and optical microscope (inset) images of the CVD-grown ${\mathrm{MoS}}_2$.

Figure 2

PL (black) and reflectance (red) of the CVD-grown ${\mathrm{MoS}}_2$. The blue lines indicate the exciton levels.

Figure 3

(a) Azimuthal symmetry of ${\mathrm{MoS}}_2$ as probed by SHG polarization dependence showing both the parallel (blue dots) and perpendicular (red dots) polarization components overlaid with their respective fits (colored curves). (b) SHG polarization dependence for three excitation spots across arbitrary 250-$\mu \mathrm{m}$ translation of the sample.

Figure 4

(a) Broadband SHG spectra of the ${\mathrm{MoS}}_2$ monolayer (red traces) and $z$-cut quartz (blue traces). Dashed lines indicate where the ratios of SHG intensities were taken to estimate ${\chi }^{\left(2\right)}$. The solid trace is a semilog plot of the PL spectrum of ${\mathrm{MoS}}_2$, indicating the positions of the $A$ and $B$ excitons, respectively. Green arrows roughly mark minimum SHG wavelengths in bulk quartz due to the spectral Maker fringe effect. (b) Theoretical $|{\chi }^{\left(2\right)}|$ dispersion calculated by DFT (black). Both real (red) and imaginary (blue) parts are also shown together with associated transitions. Two vertical lines denote half and full band gap at $K$ point. Labels for peaks are those associated with transition in band structure.