  Coherent thermal transport in nanopatterned structures is a topic of
considerable interest, but whether it occurs in certain structures remains
unclear due to poor understanding of which phonons conduct heat. Here, we
perform the first fully three-dimensional, frequency-dependent simulations of
thermal transport in nanomeshes by solving the Boltzmann transport equation
with a novel, efficient Monte Carlo method. From the spectral information in
our simulations, we show that thermal transport in nanostructures that can be
created with available lithographic techniques is dominated by incoherent
boundary scattering at room temperature. Our result provides important insights
into the conditions required for coherent thermal transport to occur in
artificial structures.
