Nonlinear Optical Properties of Transition-Metal Dichalcogenide MX2 (M = Mo, W; X = S, Se) Monolayers and Trilayers from First-Principles Calculations

Because of the absence of interlayer coupling and inversion symmetry, transition-metal dichalcogenide (MX 2 ) semiconductor monolayers exhibit novel properties that are distinctly different from their bulk crystals such as direct optical band gaps, large band spin splittings, spin-valley coupling, and piezoelectric and nonlinear optical responses and thus have promising applications in, for example, optoelectronic and spintronic devices. Here, we have performed a systematic first-principles study of the second-order nonlinear optical properties of MX 2 (M = Mo, W; X = S, Se) monolayers and trilayers within the density functional theory with the generalized gradient approximation plus scissors correction. We find that all the four MX 2 monolayers possess large second-order optical susceptibility χ (2) in the optical frequency range and significant linear electro-optical coefficients in the low-frequency limit, thus indicating their potential applications in nonlinear optical devices and electric optical switches. The χ (2) spectra of the MX 2 trilayers are overall similar to the corresponding MX 2 monolayers, albeit with the magnitude reduced by roughly a factor of 3. The prominent features in the χ (2) spectra of the MX 2 multilayers are analyzed in terms of the underlying band structures and optical dielectric function and are also compared with available experiments.