Recently, few-layer transition metal dichalcogenides (TMDCs) have been found to possess unique electronic states and have been applied to electronic and optical devices. In particular, monolayer TMDCs have been found to have a nonlinear susceptibility in the C exciton region that is three orders of magnitude higher than that of conventional nonlinear optical devices such as BBO, and applications to nonlinear optical devices are expected [1-2]. The optical second harmonic generation (SHG) spectra in the C exciton region of these monolayer TMDCs have resonance peaks at approximately the same photon energy as those of differential reflectance (DR) spectra, but there are multiple peaks that are not observed in the DR spectra [3]. The conventional interpretation of the optical modes in the C exciton region is the optical transitions near the Γ point attributed to band nesting effects, but the origin of the multi-peak structure is not yet well understood. In this study we focused on the fact that van der Waals interactions between the layers of TMDCs can modify their band structure, and observed the SHG spectra of monolayer (ML-) and few-layer (FL-) MoS₂, as well as ML- and FL-WS₂.

ML- and FL-MoS₂, as well as ML- and FL-WS₂, were transferred to SiO2/Si(001) substrates by mechanical exfoliation of single crystals, and the number of layers in each domain is identified with Raman microspectroscopy measurements. SHG microspectroscopy in the two-photon energy range from 2.4 eV to 3.2 eV was performed using an optical microscope. The fundamental light emitted from a Ti:sapphire laser (power 0.3 mW) was incident onto the microscope, and the SHG signal reflected from the sample was passed through a spectrometer and detected with a photomultiplier tube.

The SHG spectra of a monolayer (ML-) MoS₂, a trilayer (3L-) MoS2 with 3R structure, a 3L-MoS₂ with 2H structure, a ML-WS₂, a bilayer (2L-) WS₂ with 3R structure, and a five-layer (5L-) WS₂ with 2H structure are shown in Figures 1(a)-(f), respectively. The blue dots are the measured signals, indicating that there are two resonance peaks in the C exciton region. We performed curve fitting using a linear combination of two Lorentz functions. The blue lines are the fitted curves. The light blue and purple curves are the peaks, labeled as C1 and C2, respectively.

The energy of the C1 peak in FL-MoS₂ (3L-3R and 3L-2H) was shifted 0.04 eV lower from the C1 peak in ML-MoS₂, and the energy of the C1 peak in FL-WS₂ (2L-3R and 5L-2H) was shifted 0.10 eV lower from the C1 peak in ML-WS₂. These behaviors indicate that the C1 peak originated from the interband transition in the ring-shaped region, where band nesting occurred near the Γ point [4], like the C exciton in the linear optical spectrum. In contrast, for the C2 peak energy, the difference between FL and ML was small for both MoS₂ and WS₂. These behaviors indicate that the C2 peak is different from the C exciton in the linear optical spectrum and originates from excitation in a region where the band structure has changed little due to interlayer coupling. This peak can be described as a transition to a hidden state, which is specific to nonlinear optical processes. No significant structural difference was observed between the spectra of the two types of stacking structures, 3R and 2H.

In conclusion, we measured and analyzed the SHG spectra of ML- and FL-MoS₂, and ML- and FL-WS₂, and observed distinct resonance peaks called the C1 and C2 peaks.

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