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Phonon Transport in Patterned Two-Dimensional Materials from First Principles

Phonon size effects induce ballistic transport in nanomaterials, challenging Fourier's law. Nondiffusive heat transport is captured by the Peierls-Boltzmann transport equation (BTE), commonly solved under the relaxation time approximation (RTA), which assumes diagonal scattering operator. Although the RTA is accurate for many relevant materials over a wide range of temperatures, such as silicon, it underpredicts thermal transport in most two-dimensional (2D) systems, notoriously graphene. Here we present a formalism, based on the BTE with the full collision matrix, for computing the effective thermal conductivity of arbitrarily patterned 2D materials. We apply our approach to porous graphene and find strong heat transport suppression in configurations with feature sizes of the order of micrometers; this result, which is rooted in the large generalized phonon MFPs in graphene, corroborates the possibility of strong thermal transport tunability by relatively coarse patterning. Lastly, we present a promising material configuration with low thermal conductivity. Our method enables the parameter-free design of 2D materials for thermoelectric and thermal routing applications.