Understanding the Role of Four-Phonon Scattering in the Lattice Thermal Transport of Monolayer MoS$_{2}$

Abstract: In the calculations of lattice thermal conductivity ($\kappa_{\text{L}}$), vital contributions stemming from four-phonon scattering are often neglected. The significance of four-phonon scattering in the thermal transport properties of monolayer (ML) 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 $\kappa{\text{L}}$ is found to be significantly overestimated ($\sim$ 115.8 Wm$^{-1}$K$^{-1}$ at 300 K). With the incorporation of the four-phonon scattering processes, the $\kappa_{\text{L}}$ reduces to 24.6 Wm$^{-1}$K$^{-1}$, which is found to be closer to the experimentally measured $\kappa_{\text{L}}$ of 34.5 Wm$^{-1}$K$^{-1}$. Four-phonon scattering significantly impacts the carrier lifetime ($\tau$) of the low-energy out-of-plane acoustic mode (ZA) phonons and thereby, suppresses its contribution in $\kappa_{\text{L}}$ from 64% (for three-phonon scattering) to 16% (for both three- and four-phonon scatterings). The unusually high four-phonon scattering rate ($\tau_{4}^{-1}$) of the ZA phonons is found to result from the simultaneous effect of the acoustic-optical frequency gap, strong anharmonicity, and the reflection symmetry imposed selection rule. The strong coupling between the quadratic dispersion of the ZA mode and the $\tau_{4}^{-1}$ is discovered by 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 the strained ML-MoS${2}$, both qualitatively and quantitatively. These conclusions will provide significant insights into the thermal transport phenomena in ML-MoS${2}$, as well as any other 2D material.