  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.

Mesoscale and Nanoscale Physics;Materials Science