Exceptional four-phonon scattering effects on low-temperature thermal conductivity in two-dimensional materials

First-principles-based predictions of lattice thermal conductivity (TC) from perturbation theory have achieved significant success. Usually, it only includes three-phonon (3ph) scattering processes; only recently, four-phonon (4ph) scattering processes have been found to have an impact that is comparable to 3ph scattering at medium and high temperatures in various materials, while the influence of 4ph scattering on TC at low temperatures is generally believed to be insignificant. By combining the first-principles calculations, machine-learning techniques, and Boltzmann transport equation, we find that there are unusually strong 4ph processes even in the low-frequency range of two-dimensional (2D) materials such as h-$X\mathrm{N}$ ($X=\mathrm{B}$, Al, Ga), which have a remarkable influence on the low-temperature TC. Such strong 4ph processes originate from the out-of-plane acoustic (ZA) phonon mode of 2D materials. Furthermore, we find that the intensity of 4ph scattering and thus TC can be effectively manipulated by changing the dispersion of the ZA phonon mode, which can be easily achieved through strain engineering. The present study provides distinct insights into low-temperature phonon transport and its manipulation in 2D materials.