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Defect-modified acoustic phonons in a single layer of MoS2

Aleksandar Radic, Boyao Liu, Akshay Rao, Sam Lambrick

TL;DR

This work addresses the unexpectedly poor thermal transport in atomically thin MoS2 by directly measuring low-energy acoustic phonons in a quasi-freestanding monolayer using Helium-3 spin-echo spectroscopy. The authors map the flexural and hybrid Rayleigh wave dispersions, extract mechanical parameters such as the bending rigidity $\\kappa$, areal density $\\rho_{2D}$, and substrate coupling $\\omega_0$, and identify a defect-driven crossover at $q_c=0.25(0.02)$ corresponding to a defect spacing $\\lambda_c\\approx1.9$ nm. They observe defect-induced Van Hove singularities and strongly suppressed group velocities, and they measure phonon linewidths that yield lifetimes $\\tau_{flex}\\approx1.21$ ps and mean-free paths $\\Lambda_{flex}\\approx1.68$ nm, consistent with a defect density around $2.8\\times10^{13}$ cm⁻². The results support the prominence of four-phonon processes in 2D MoS2 thermal transport and demonstrate how atomic-scale disorder governs energy flow in vdW materials, offering a framework for disorder-engineered control of heat conduction.

Abstract

The thermal, mechanical, and electronic performance of atomically thin semiconductors is governed by their low-energy phonons, yet the impact of atomic-scale disorder on these modes remains poorly understood. Here, we report the first measurement of acoustic phonon dispersions in a quasi-freestanding monolayer semiconductor (MoS2), using helium-3 spin-echo spectroscopy. We identify a defect-driven regime change at a critical wavevector, $q_c$, marking the breakdown of continuum elastic behavior. At this length scale, the flexural mode transitions from continuum bending to defect-pinned standing waves, while the hybridized Rayleigh wave becomes vibrationally disordered in its dispersion and linewidth. We observe multiple defect-induced Van Hove singularities deep within the Brillouin zone and strongly suppressed acoustic group velocities, providing direct experimental evidence that four-phonon processes drive thermal transport in mono- and few-layer MoS2. These results offer a microscopic explanation for the anomalously low thermal conductivity widely observed in transition-metal dichalcogenides and demonstrate how atomic-scale disorder dictates energy flow in two-dimensional materials.

Defect-modified acoustic phonons in a single layer of MoS2

TL;DR

This work addresses the unexpectedly poor thermal transport in atomically thin MoS2 by directly measuring low-energy acoustic phonons in a quasi-freestanding monolayer using Helium-3 spin-echo spectroscopy. The authors map the flexural and hybrid Rayleigh wave dispersions, extract mechanical parameters such as the bending rigidity , areal density , and substrate coupling , and identify a defect-driven crossover at corresponding to a defect spacing nm. They observe defect-induced Van Hove singularities and strongly suppressed group velocities, and they measure phonon linewidths that yield lifetimes ps and mean-free paths nm, consistent with a defect density around cm⁻². The results support the prominence of four-phonon processes in 2D MoS2 thermal transport and demonstrate how atomic-scale disorder governs energy flow in vdW materials, offering a framework for disorder-engineered control of heat conduction.

Abstract

The thermal, mechanical, and electronic performance of atomically thin semiconductors is governed by their low-energy phonons, yet the impact of atomic-scale disorder on these modes remains poorly understood. Here, we report the first measurement of acoustic phonon dispersions in a quasi-freestanding monolayer semiconductor (MoS2), using helium-3 spin-echo spectroscopy. We identify a defect-driven regime change at a critical wavevector, , marking the breakdown of continuum elastic behavior. At this length scale, the flexural mode transitions from continuum bending to defect-pinned standing waves, while the hybridized Rayleigh wave becomes vibrationally disordered in its dispersion and linewidth. We observe multiple defect-induced Van Hove singularities deep within the Brillouin zone and strongly suppressed acoustic group velocities, providing direct experimental evidence that four-phonon processes drive thermal transport in mono- and few-layer MoS2. These results offer a microscopic explanation for the anomalously low thermal conductivity widely observed in transition-metal dichalcogenides and demonstrate how atomic-scale disorder dictates energy flow in two-dimensional materials.

Paper Structure

This paper contains 10 sections, 8 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Helium-3 spin-echo spectroscopy
  3. Results
  4. Mechanical properties of a single layer of MoS2
  5. Defect-phonon scattering and Van Hove singularities
  6. Phonon linewidths without local thermal effects
  7. The microscopic origins of poor thermal conductivity in few-layer TMDs
  8. Conclusion
  9. Phonon dispersion fitting
  10. Calculation of the vibrational density of states (VDOS)

Figures (3)

  • Figure 1: Schematic of helium-3 spin-echo (HeSE) spectroscopy. The topmost layer of bulk MoS2 vibrates as a quasi-freestanding monolayer due to weak interlayer van der Waals (vdW) binding. The spins of the incident 3He are polarized and precession induced by a solenoidal magnetic field ($B_i$). During scattering the atoms can exchange energy with the surface, exciting or destroying surface phonons. The final energy distribution is measured in the time domain via the atoms' perpendicular spin polarizations ($P_x,P_y$).
  • Figure 2: (a) Dispersion curves for flexural (circles) and hybrid Rayleigh Wave (hRW) (diamonds) modes of quasi-freestanding ML-MoS2 along $\overrightarrow{\Gamma K}$. For $q\leq 0.25$ (vertical dashed line) the out-of-plane mode is well-described as a flexural mode from elastic membrane theory (Eqn. \ref{['eqn:flexural']}Amorim2013FlexuralSubstrate) and the hRW is non-dispersive due to dominant defect scattering. For $q\geq 0.25$ both modes have positive linear dispersions. The regime change (vertical dashed line at $q_c=0.25\pm0.02$) occurs at a characteristic length $\lambda_c\sim1.90\pm0.15nm$ that we attribute to the characteristic length between defects. Inset shows the creation of a Van Hove singularity (VHs) around $q_c$ in the flexural mode, corresponding to feature A in panel (b). (b) 1D Vibrational density of states (VDOS) along $\overrightarrow{\Gamma K}$ calculated from experimental dispersions reveals three VHs labeled A, B and C. VHs A and B arise from defect-phonon scattering, forming large enhancements in the VDOS away from any high symmetry points that will significantly affect thermal transport. VHs C is expected from elastic membrane theory due to the parabolic dispersion lineshape flattening near $\Gamma$. All data measured at $120\degreeCelsius$. Fitting and calculation details for dispersions and VDOS are presented in the End Matter along with sample and measurement details.
  • Figure 3: Example phonon linewidths of the flexural (blue) and hybridized Rayleigh Wave (hRW, red) near $\Gamma$ ($q=0.02$). The flexural mode is described by a Lorentzian linewidth $\gamma = 0.54(5)meV$ ($4.36(41)\per cm$). The hRW has an ill-defined linewidth as expected in a non-dispersive region ($q<q_c$). An asymmetric Gaussian is shown to guide the eye. We note that the flexural mode is always measured as an creation peak ($-\mathrm{ive}\,\Delta E$) whereas the hRW is annihilation-type. Data has been normalised and scaled for visual clarity.