Role of Interlayer Coupling in the Second Harmonic Generation of Bilayer Transition-metal Dichalcogenides

TL;DR

This study investigates how weak interlayer coupling influences second harmonic generation in bilayer transition-metal dichalcogenides using first-principles calculations, revealing how interlayer hopping strength affects SHG responses.

Contribution

It provides a systematic analysis of interlayer coupling effects on SHG in bilayer TMDs, explaining experimental observations and guiding the design of controllable SHG in vdW systems.

Findings

SHG intensity at zero frequency is affected by band repulsion and interlayer hopping.

SHG spectra are highly sensitive to interlayer coupling in low photon-energy regions.

Interlayer coupling influences SHG peak variations across different bilayer TMDs.

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 article, taking homo-bilayer $MoS_2/MoS_2$ and hetero-bilayer $MoS_2/MoSe_2$ as typical examples, we have systemically investigated their SHG susceptibilities as a function of interlayer hopping strength using first-principles calculations. For the SHG at zero frequency limit of both $MoS_2/MoS_2$ and $MoS_2/MoSe_2$, although the increase of tint can increase the intensities of interlayer optical transitions (IOT), the increased band repulsion around G point can eventually decrease their SHG values; the larger the tint, the smaller the SHG response. For the SHG spectra of $MoS_2/MoSe_2$ in the low photon-energy region, opposite to the $MoS_2/MoS_2$, their peak values are very sensitive to the variable tint, due to the strong $t_{int}$-dependent IOT dominating in the band edge; the larger the tint, the larger the SHG. For the SHG of $MoS_2/MoS_2$ in the high photon-energy region, comparing to the $MoS_2/MoSe_2$, their peak values will decrease in a much more noticeable way as the $t_{int}$ 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 tint, but also may provide a general understanding for designing controllable the SHG effects in the vdW systems.