Unveiling layer-dependent interlayer coupling and vibrational properties in MoTe2 under high pressure

Layered materials have garnered significant attention for their ability to exhibit tunable physical properties through stacking, twisted angles, and interlayer coupling. The interlayer vibrations in these materials are highly sensitive to, and can be controlled by, their thickness. However, the layer-dependent interlayer vibration behavior under high pressure remains unclear. Here, we investigate the layer-dependent high-pressure Raman spectroscopy of 1--5L and bulk $\mathrm{Mo}{\mathrm{Te}}_{2}$ up to 14-GPa pressure, and demonstrate a pressure-induced thickness-dependent interlayer vibration behavior. We observe the pressure-induced blueshift rates of the breathing (LB) and shear (S) modes exhibit opposite strong layer-dependent behaviors, which arise from thickness-dependent interlayer coupling and restoring forces, respectively. Furthermore, we propose a pressure-dependent linear chain model to characterize the force constants under pressure and employ a bond-polarization model to explain the intensity changeover between the S and LB modes, as well as between the ${A}_{1}\ensuremath{'}/{A}_{1g}^{2}$ and ${E}^{\ensuremath{'}}/E{{}_{g}}^{1}$ modes, which is attributed to the increase in interlayer Te--Te bond angle and intralayer distance between Mo and Te atomic layers, respectively. Our findings elucidate the robust thickness-dependent interlayer vibrations in $\mathrm{Mo}{\mathrm{Te}}_{2}$ and provide a firm foundation for exploring and characterizing interlayer coupling through pressure engineering in van der Waals materials.