Unveiling layer-dependent interlayer coupling and vibrational properties in $\mathrm{Mo}{\mathrm{Te}}_2$ 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 $A_1\prime /A_{1g}^2$ and $E^{\prime }/E{{}_g}^1$ 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.

Figure 1

Layer-dependent Raman spectra of $\mathrm{Mo}{\mathrm{Te}}_2$ at ambient pressure. (a) Schematic diagram of diamond-anvil cell (DAC) device used for the experiments. (b) Optical image of few-layer $\mathrm{Mo}{\mathrm{Te}}_2$ samples, including 1L, 2L, 3L, and 4L $\mathrm{Mo}{\mathrm{Te}}_2$. (c) Crystal structure of $\mathrm{Mo}{\mathrm{Te}}_2$, illustrating arrangement of Mo (lilac) and Te (yellowish-brown) atoms. Distances between adjacent Te atomic layers (interlayer) and between Mo and Te atomic layers (intralayer) are denoted as $d$ and $l$, respectively. Angle (θ) is formed by adjacent interlayer Te–Te bonds and out-of-plane direction. (d) Raman spectra of $\mathrm{Mo}{\mathrm{Te}}_2$ as function of layer number. Circle points and solid lines represent measured data and smoothing data (Loess method with window ratio of 0.008), respectively. (e) Layer-dependent Raman peak positions of $\mathrm{Mo}{\mathrm{Te}}_2$. Low-frequency shear- and breathing modes exhibit blue- and redshifts, respectively, as layer number increases, consistent with results obtained from LCM.

Figure 2

Pressure-dependent low-frequency Raman spectra in layer-dependent $\mathrm{Mo}{\mathrm{Te}}_2$. (a)–(c) Color plots depicting progressive changes in Raman spectra with increasing pressure for different layer thicknesses: (a) bilayer (2L) $\mathrm{Mo}{\mathrm{Te}}_2$, (b) trilayer (3L) $\mathrm{Mo}{\mathrm{Te}}_2$, (c) four layer (4L) $\mathrm{Mo}{\mathrm{Te}}_2$, and (d) five layer (5L) $\mathrm{Mo}{\mathrm{Te}}_2$. (e) Pressure-dependent variations in positions of the breathing (LB) modes. (f) Pressure-dependent variations in positions of shear (S) modes. All S and LB modes consistently exhibit blueshift as applied pressure intensifies.

Figure 3

Layer-dependent peak positions of S and LB modes in $\mathrm{Mo}{\mathrm{Te}}_2$ under pressure. (a), (b) Normalized Raman peak positions of (a) LB and (b) S modes with different thickness as function of pressure, relative to peak position at ambient pressure. Values are denoted as $\mathrm{\Delta }\omega ={\omega }_p-{\omega }_0$, where ${\omega }_p$ and ${\omega }_0$ are frequencies of LB and S modes at high pressure and ambient pressure, respectively. (c) Layer-dependent calculated interlayer distance (blue line) and coefficients A for S and LB modes (red lines). (d) Pressure-dependent force constant calculated from p-LCM (red lines) and calculated interlayer ($d$) and intralayer ($l$) spacing distances of bulk $\mathrm{Mo}{\mathrm{Te}}_2$ (blue lines). (e), (f) Vibration patterns of (e) LB and (f) S modes. $F_R$ denotes restoring force.

Figure 4

Pressure-induced intensity changeover between S and LB modes of $\mathrm{Mo}{\mathrm{Te}}_2$. (a), (b) Raman peak position of (a) LB and (b) S modes of few-layer $\mathrm{Mo}{\mathrm{Te}}_2$. Points represent measured data, while lines denote simulated results of p-LCM. (c) Intensity ratio between S and LB modes ($I_{\mathrm{S}}/I_{\mathrm{LB}}$) of 2L (green), 4L (red), and 5L (blue) $\mathrm{Mo}{\mathrm{Te}}_2$. Lines are provided as visual guides. (d) Calculated pressure-dependent angle (θ) by first-principle calculations (blue curves) and estimated $I_{\mathrm{S}}/I_{\mathrm{LB}}$ of 2L, 4L, and 5L $\mathrm{Mo}{\mathrm{Te}}_2$ by bond-polarization model (red curves). (e) Frequency difference between LB and S modes of 2L, 4L, and 5L $\mathrm{Mo}{\mathrm{Te}}_2$ as function of pressure.

Figure 5

High-frequency Raman spectra of $\mathrm{Mo}{\mathrm{Te}}_2$ under pressure. (a) Pressure-dependent Raman spectra of 5L $\mathrm{Mo}{\mathrm{Te}}_2$ in wave-number range of $100-400\mathrm{c}{\mathrm{m}}^{-1}$. (b)–(d) Pressure evolution of high-frequency Raman peak positions for (b) $E^{\prime }/E_g^1$, (c) $A_2^{{}^{″}}/A_{1g}^1$, and (d) $A_1\prime /A_{1g}^2$ modes. Experimental data points were extracted from Raman spectra, and solid curves represent fitted results for visual guidance. All of these vibration modes exhibit a blueshift with increasing pressure. (e) Intensity ratio between $A_1\prime /A_{1g}^2$ and $E^{\prime }/E_g^1$ modes ($I_{A_{1g}}/I_{E_{2g}^1}$) for 2–5 L and bulk $\mathrm{Mo}{\mathrm{Te}}_2$, showing an increasing trend with increasing pressure.