Ballistic Thermal Conductance in Layered Two-Dimensional Materials

The thermal properties of two-dimensional (2D) materials like graphene, h-BN, MoS$_{\mathrm{2}}$ and WS$_{\mathrm{2}}$ are uniquely anisotropic, including high in-plane but low out-of-plane thermal conductivity $\kappa $. Here we provide a comparative study of the ballistic limits of heat flow in these 2D layers and stacks. Based on full phonon dispersions from density functional theory, we calculate their in-plane and cross-plane ballistic thermal conductance per cross-sectional area, $G$. For a given material, monolayers and multilayers have similar in-plane $G$ above 100 K, but monolayers show higher $G$ at low temperature due to the contribution of flexural phonons. At 300 K, graphene has the highest $G$ $\sim$ 4.2 GWK$^{\mathrm{-1}}$m$^{\mathrm{-2}}$, about 20{\%} higher than h-BN and 5 times higher than MoS$_{\mathrm{2}}$ and WS$_{\mathrm{2}}$. Cross-plane values are about one order of magnitude lower than in-plane values due to weak van der Waals interactions. Based on the calculated $G$, we can obtain phonon mean free path, given diffusive $\kappa $. These results are important as they establish the length scales of the ballistic-diffusive transition of heat flow and the non-classical regime where $\kappa $ depends on the system size.