Role of interlayer coupling in second harmonic generation in bilayer transition metal dichalcogenides

Abstract

Little is known about the role of weak interlayer coupling in the second harmonic generation (SHG) effects of two-dimensional van der Waals (vdW) systems. In this paper, taking homobilayer $\mathrm{Mo}{\mathrm{S}}_{2}/\mathrm{Mo}{\mathrm{S}}_{2}$ and heterobilayer $\mathrm{Mo}{\mathrm{S}}_{2}/\mathrm{Mo}{\mathrm{Se}}_{2}$ as typical examples, we have systemically investigated their SHG susceptibilities ${\ensuremath{\chi}}^{(2)}$ as a function of interlayer hopping strength (${t}_{\mathrm{int}}$) using first-principles calculations. For the ${\ensuremath{\chi}}_{yyy}^{(2)}(0;0,0)$ of both $\mathrm{Mo}{\mathrm{S}}_{2}/\mathrm{Mo}{\mathrm{S}}_{2}$ and $\mathrm{Mo}{\mathrm{S}}_{2}/\mathrm{Mo}{\mathrm{Se}}_{2}$, although the increase of ${t}_{\mathrm{int}}$ can increase the intensities of interlayer optical transitions (IOT), the increased band repulsion around the \ensuremath{\Gamma} point can eventually decrease their ${\ensuremath{\chi}}_{yyy}^{(2)}(0;0,0)$ values; the larger the ${t}_{\mathrm{int}}$, the smaller the ${\ensuremath{\chi}}_{yyy}^{(2)}(0;0,0)$. For the $|{\ensuremath{\chi}}_{yyy}^{(2)}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})|$ spectra of $\mathrm{Mo}{\mathrm{S}}_{2}/\mathrm{Mo}{\mathrm{Se}}_{2}$ in the low photon-energy region, opposite to the $\mathrm{Mo}{\mathrm{S}}_{2}/\mathrm{Mo}{\mathrm{S}}_{2}$, their peak values are very sensitive to the variable ${t}_{\mathrm{int}}$, due to the strong ${t}_{\mathrm{int}}$-dependent IOT dominating in the band edge; the larger the ${t}_{\mathrm{int}}$, the larger the $|{\ensuremath{\chi}}_{yyy}^{(2)}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})|$. For the $|{\ensuremath{\chi}}_{yyy}^{(2)}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})|$ of $\mathrm{Mo}{\mathrm{S}}_{2}/\mathrm{Mo}{\mathrm{S}}_{2}$ in the high photon-energy region, comparing to the $\mathrm{Mo}{\mathrm{S}}_{2}/\mathrm{Mo}{\mathrm{Se}}_{2}$, their peak values will decrease in a much more noticeable way as the ${t}_{\mathrm{int}}$ increases, due to the larger reduction of band-nesting effect. Our study not only can successfully explain the puzzling experimental observations for the different SHG responses in different bilayer transition metal dichalcogenides under variable ${t}_{\mathrm{int}}$, but also may provide a general understanding for designing controllable the SHG effects in the vdW systems.

Topics & Concepts