Understanding the role of four-phonon scattering in the lattice thermal transport of monolayer MoS2

In the calculations of lattice thermal conductivity (${\ensuremath{\kappa}}_{\text{L}}$), vital contributions stemming from four-phonon scattering is often neglected. The significance of four-phonon scattering in the thermal transport properties of monolayer (ML) ${\mathrm{MoS}}_{2}$ has been unraveled using first-principles calculations combined with the Boltzmann transport equation. If only three-phonon scattering processes are considered then the ${\ensuremath{\kappa}}_{\text{L}}$ is found to be significantly overestimated ($\ensuremath{\sim}115.8\phantom{\rule{4pt}{0ex}}{\mathrm{W}\phantom{\rule{0.16em}{0ex}}\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at 300 K). With the incorporation of the four-phonon scattering processes, the ${\ensuremath{\kappa}}_{\text{L}}$ reduces to 24.6 ${\mathrm{W}\phantom{\rule{0.16em}{0ex}}\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$, which is found to be closer to the experimentally measured ${\ensuremath{\kappa}}_{\text{L}}$ of 34.5 ${\mathrm{W}\phantom{\rule{0.16em}{0ex}}\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$. Four-phonon scattering significantly impacts the carrier lifetime ($\ensuremath{\tau}$) of the low-energy out-of-plane acoustic mode (ZA) phonons and thereby, suppresses its contribution in ${\ensuremath{\kappa}}_{\text{L}}$ from 64% (for three-phonon scattering) to 16% (for both three- and four-phonon scatterings). The unusually high four-phonon scattering rate (${\ensuremath{\tau}}_{4}^{\ensuremath{-}1}$) of the ZA phonons is attributed to the distinctive quadratic dispersion, along with the combined effects of the acoustic-optical frequency gap, strong anharmonicity, and the selection rule imposed by reflection symmetry. The strong coupling between the dispersion characteristics of the ZA mode and the ${\ensuremath{\tau}}_{4}^{\ensuremath{-}1}$ is discovered through the application of mechanical strain. The strain induced increase in the linearity of the ZA mode dispersion dramatically reduces the significance of the four-phonon scattering in ML-${\mathrm{MoS}}_{2}$, both qualitatively and quantitatively. These findings offer valuable insights into the thermal transport phenomena of ML-${\mathrm{MoS}}_{2}$, as well as other 2D materials.