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First principles-based predictions of lattice thermal conductivity (TC) fromperturbation theory have achieved significant success. In general, it onlyincludes three-phonon (3ph) scattering. However, recent studies have revealedthat four-phonon (4ph) scattering, treated under single-mode relaxation timeapproximation (RTA), has a comparable impact to 3ph scattering at medium andhigh temperatures in various materials, particularly in two-dimensional (2D)materials. Nonetheless, the influence of 4ph scattering on TC at lowtemperatures has not been explored so far, owing to the assumption that 4phprocesses are generally insignificant at low temperatures. By combining thefirst-principles calculations, machine learning techniques, Boltzmann transportequation (BTE), and molecular dynamics (MD) simulations, we find that there areunusually strong 4ph processes in the low-frequency range of 2D materials suchas h-XN (X=B, Al, Ga), which have remarkable influence on the low-temperatureTC. We also find that the strong 4ph processes are originated from the flexuralout-of-plane acoustic (ZA) phonon mode of 2D materials. We further discover theremarkable normal (N) processes of 4ph scattering in 2D materials, which makethe conventionally adopted perturbation methods for TC calculation far fromsufficient at low temperatures. Finally, we find that the intensity of 4phscattering and thus TC can be effectively manipulated by changing thedispersion of ZA phonon mode, which can be easily achieved through strainengineering. Our study provides new insights into low-temperature phonontransport and its manipulation in 2D materials.

Strong four-phonon processes on thermal conductivity of two-dimensional materials in the low-temperature region