How Hydrodynamic Phonon Transport Determines the Convergence of Thermal Conductivity in Two-Dimensional Materials

The phonon Boltzmann transport equation combined with first-principles calculation has achieved great success in exploring the lattice thermal conductivity (κ) of various materials. However, the convergence of the predicted κ is a critical issue, leading to quite scattered results recorded in the literature, even for the same material. In this paper, we explore the origin for the convergence of thermal conductivity in two-dimensional (2D) materials. Two kinds of typical 2D materials, graphene and silicene, are studied, and the bulk silicon is also compared as a control system for a three-dimensional material. The effect of the cutoff radius (rc) in the third-order interatomic force constants on κ is studied for these three materials. It is found that that κ of these three materials exhibits diverse convergence behaviors with respect to rc, which coincides very well with the strength of hydrodynamic phonon transport. By further analyzing the phonon lifetime and scattering rates, we reveal that the dominance of the normal scattering process gives rise to the hydrodynamic phonon transport in both graphene and silicene, which results in long-range interaction and a large lifetime of low-frequency flexural acoustic phonons, while the same phenomenon is absent in bulk silicon. Our study highlights the importance of long-range interaction associated with hydrodynamic phonon transport in determining the thermal conductivity of 2D materials.