Tuning Terahertz Optomechanics of MoS2 Bilayers with Homogeneous In-plane Strain

TL;DR

The work investigates how homogeneous in-plane biaxial tensile strain tunes terahertz optomechanics in MoS$_2$ bilayers grown under high-temperature conditions. By combining PVD growth with ultralow-frequency Raman spectroscopy and polarization-resolved SHG, it demonstrates that in-plane strain induces a vertical contraction of the vdW gap, dramatically hardening the interlayer breathing mode with a Grüneisen parameter in the range $\\gamma_{out} \\approx 10-14$ and an effective Poisson's ratio $\\nu_{eff} \\approx 0.19-0.24$. Ab initio calculations qualitatively reproduce the breathing-mode hardening and vertical contraction, though the quantitative shifts depend on the vdW treatment, highlighting challenges in capturing anharmonic vdW coupling. The results establish MoS$_2$ bilayers as a highly tunable THz optomechanical platform where in-plane strain acts as a precise lever to control interlayer coupling and exciton hybridization, with implications for moiré physics, strain-engineered devices, and polarization-sensitive light–matter interactions, all without external pressure.

Abstract

Homogeneous in-plane biaxial tensile strain strengthens the out-of-plane van der Waals interaction in \MoS\ bilayers (BLs) and can be used to fine-tune their terahertz (THz) oscillations. Using ultralow-frequency Raman spectroscopy on hexagonal (2H) and rhombohedral (2R) stacked BLs, we observe a hardening of the interlayer breathing modes originating from a strain-induced Poisson contraction of the vdW separation between the layers, and characterized by an effective out-of-plane Poisson's ratio of $ν_\mathrm{eff} \approx 0.19\text{--}0.24$. Strikingly, this geometric contraction drives the system into a highly repulsive regime of the intermolecular potential, corresponding to a Grüneisen parameter of $γ\approx 10\text{--}14$. This value surpasses even the `giant' one reported for phosphorene, establishing these van der Waals BLs as highly tunable nonlinear mechanical platforms that can be addressed at the THz regime, couple strongly with light, and do not need external pressure knobs.

Figures (12)

• Figure 1: (a) Optical contrast images of 2H and 2R MoS$_2$ BLs grown on a SiO$_{2}$ substrate. (b) SHG spectra for monolayer, 2H and 2R bilayers. Insets are ball and stick models. (c) SHG intensity maps in monolayer and BL regions.
• Figure 2: (a) Correlation between $A_{1g}$ and $E_{2g}^1$ peak positions for MLs (small circles) and 2H BLs (small squares), including average values (large circles and squares). The black circle (square) corresponds to samples where the strain was released after transferring a MoS$_{2}$ ML (BL) onto another SiO$_{2}$ substrate. (b) $E_{2g}^1$ and (c) $A_{1g}$ mode frequencies from DFT calculations for 2H (orange) and 2R (light blue) phases, respectively. Both modes red-shift under in-plane biaxial strain.
• Figure 3: (a) Raman spectrum of a MoS$_{2}$ ML on SiO$_{2}$. (b) Raman spectrum of a 2R BL on SiO$_{2}$; the magnified view between $-1.5$ and 1.5 THz shows signatures of shear ($E_{2g}^2$) and breathing ($B_{2g}$) modes absent in the monolayer. (c) Strain-free phonon dispersion for a 2R bilayer. Raman-active high- and low-frequency modes are highlighted on insets. (d) Low-frequency Raman spectrum of 2H phase on SiO$_{2}$.
• Figure 4: Experimental evolution of the (a) $B_{2g}$ and (b) $E_{2g}^2$ frequencies for 2H-stacked $\mathrm{MoS_{2}}$ BLs under varying biaxial tensile strain. (c) DFT calculations of the breathing (black) and shear (orange) mode frequencies for 2H MoS$_{2}$. (d) Interlayer distance $d$vs. in-plane biaxial strain.
• Figure S1: Phonon dispersion of a strain-free 2H-MoS$_{2}$ bilayer. The low and high frequency modes near $\Gamma$ are highlighted in the two panels on the right.