Acoustic Guided Waves in MoS2 thin flakes

Abstract

Guided acoustic waves in two-dimensional materials are a key channel for energy transport and dissipation, yet their generation and propagation in transition metal dichalcogenides remain poorly understood. Here, we employ in-situ and spatially decoupled ultra-fast optical pump-probe techniques to investigate guided waves in MoS2 flakes with thicknesses between 90 and 410 nm. We observe a propagating acoustic excitation with a constant velocity of (6.7 +/- 0.8) km/s, independent of thickness. Finite element simulations and symmetry analysis reveal that these vibrations deviate from the classical Lamb wave model and are better described as a superposition of decoupled longitudinal and shear modes. We show that their optical detectability is governed by the Poisson effect: longitudinal components modulate the flake thickness and generate a measurable signal, whereas shear motion remains largely optically invisible. An intrinsic attenuation length of approximately 3.3 microns indicates that dissipation is dominated by material-specific mechanisms rather than geometric spreading. Finally, we demonstrate remote excitation across a nanometric step, enabling acoustic generation in optically inaccessible regions. These results provide a foundation for nanoscale phononic circuits and engineered in-plane energy transport in 2D-based optomechanical and quantum acoustic devices.

Figures (14)

• Figure 1: Basic characterization of guided acoustic waves in MoS$_2$. (a) Optical transmission microscopy image of mechanically exfoliated MoS$_2$ flakes on a SiO$_2$ substrate. (b) Left: Schematic of the in situ pump–probe configuration: a 400 nm wavelength pump pulse excites acoustic vibrations in the MoS$_2$ flake, while an 800 nm wavelength probe pulse monitors the resulting changes in optical transmission induced by the lattice oscillations. Both spots are spatially overlapped on the sample surface. Right: Representative in situ differential transmission signal after thermal background subtraction (top, black solid line) and its corresponding FFT (bottom) for a 108 nm thick flake. The spectrum reveals the fundamental breathing mode at 18.9 GHz (green) and a lower-frequency guided wave component at 2.7 GHz (red). The red and green solid lines in the top panel represents a damped sine fit of the guided and breathing mode, respectively. (c) Normalized amplitude of the guided wave mode relative to the fundamental breathing mode for all in situ measurements as a function of flake thickness.
• Figure 2: Propagation and attenuation of guided waves. (a) Schematic of the spatially decoupled pump–probe configuration: a 400 nm wavelength pump pulse excites acoustic vibrations, while an 800 nm wavelength probe pulse monitors the mechanical disturbance at a distance $d$ from the excitation area. (b) Representative spatially decoupled differential transmission signals for a 347 nm thick flake after thermal background subtraction, with $d$ ranging from 1.3 µm to 6.4 µm. The signals exhibit a wave packet arriving at increasingly later times. (c) Propagation velocity extracted from different sets of spatially decoupled measurements as a function of flake thickness. The dashed red line indicates the weighted average velocity of (6.7 $\pm$ 0.8) km s$^{-1}$. (d) Amplitude of the first signal crest from panel (b) as a function of $d$. Solid and dashed black lines represent fits to exponential and geometric attenuation models, respectively, with the exponential fit yielding an attenuation coefficient $\chi$ = (3.3 $\pm$ 0.2) µm. (e) Velocity measurements performed at varying probe angles relative to the crystalline axes. The dashed red line represents the average velocity from panel (c), showing no significant in-plane anisotropy within experimental dispersion.
• Figure 3: FEM simulation results and mode analysis. (a, b) Colormaps of the simulated average absolute radial displacement ($|u_r|$) as a function of flake thickness and acoustic frequency for pump–probe distances $d$= 0 µm and 2 µm, respectively. Red and black markers indicate experimental data for in situ and decoupled measurements, respectively. Dashed lines in panel (a) represent theoretical thickness-to-frequency dispersion relationships for Lamb wave modes. (c) Simulated radial ($u_r$, top) and vertical ($u_z$, bottom) displacement profiles for a 347 nm thick MoS$_2$ film at a frequency of 3.3 GHz. The $z$-coordinate represents height, with $z$ = 0 at the SiO$_2$ substrate interface, while $r$ denotes the radial distance from the center of the excitation spot. (d) Radial displacement profile at the film surface ($z$ = 347 nm) as a function of $r$ (left) and its corresponding FFT (right). The spectral analysis reveals two distinct peaks corresponding to propagation velocities of 6.9 km s$^{-1}$ and 3.3 km s$^{-1}$, identifying the mixed longitudinal and shear nature of the radial signal.
• Figure 4: Guided wave transmission across a MoS$_2$ step. (a) Optical microscopy image of an exfoliated MoS$_2$ flake featuring two neighboring regions of different thicknesses that form a physical step. (b) AFM height profiles corresponding to the dashed lines in panel (a), revealing a step height of $\sim$80 nm (transitioning from 300 nm to 220 nm).(c) Spatially decoupled differential transmission signals measured at a pump–probe distance $d\sim$ 4 µm. The blue trace represents the signal obtained when the thicker region is pumped and the thinner region is probed, exhibiting successful wave transmission. The ocher trace shows the reciprocal configuration (pumping the thin region and probing the thick region), where no significant signal is detected above the noise floor.
• Figure S1: Optical microscopy image of mechanically exfoliated MoS$_2$ flakes on a groove-shaped holes patterned borosilicate substrate.