Anisotropic model with truncated linear dispersion for lattice and interfacial thermal transport in layered materials

Recently, an anisotropic Debye model [Dames et al., Phys. Rev. B 87, 125426 (2013)] was proposed for calculations of the interfacial thermal conductance and the minimum thermal conductivity of graphite-like layered materials. Despite successes of the model in explaining heat transport mechanisms in layered materials (e.g., phonon focusing in highly anisotropic materials), the anisotropic Debye model assumes a phonon dispersion with unrealistic speeds of sound especially for the flexural (ZA) phonons and overestimated cutoffs for all phonon branches. The deficiencies lead to substantially underestimated phonon irradiation for low-frequency phonons. Here, we develop an anisotropic model with truncated linear dispersion that resembles the real phonon dispersion, using speeds of sound derived from elastic constants and cutoff frequencies derived from Brillouin zone boundaries. We also employ a piecewise linear function for the ZA phonons. Our model correctly calculates the phonon irradiation over a wide temperature range, verifying the accuracy of our model. We compare calculations of our and the Dames' models to measurements of thermal conductivity of graphite and thermal conductance of metal/graphite interfaces, and find that the two models differ significantly for heat transport across the basal planes in graphite even at high temperatures. Our work thus provides a convenient analytical tool to study the phonon transport properties in layered materials.