  Coherent wave effects of thermal phonons hold promise of transformative
opportunities in thermal transport control but remain largely unexplored due to
the small wavelength of thermal phonons, typically below a few nanometers. This
small length scale indicates that, instead of artificial phononic crystals, a
more promising direction is to examine the coherent phonon effects in natural
materials with hierarchical superstructures matching the thermal phonon
wavelength. In this work, we use first-principles simulations to characterize
the previously unstudied thermal properties of D-graphene and T-graphene,
two-dimensional carbon allotropes based upon the traditional graphene structure
but containing a secondary, in-plane periodicity. We find that despite very
similar atomic structure and bonding strength, D-graphene and T-graphene
possess significantly different thermal properties than that of pristine
graphene. At room temperature, the calculated thermal conductivity of
D-graphene and T-graphene is 600 Wm-1K-1 and 800 Wm-1K-1 compared to over 3000
Wm-1K-1 for graphene. We attribute these distinct properties to the presence of
naturally occurring, low frequency optical phonon modes that display
characteristics of phonon coherence and arise from a folding of the acoustic
modes and the associated frequency gap opening, a phenomenon also found in
superlattices where an out of plane periodicity is introduced. Furthermore, we
observe significantly enhanced Umklapp scatterings in D- and T-graphene that
largely suppress the hydrodynamic phonon transport in pristine graphene. Our
study presents D-graphene and T-graphene as ideal model systems to explore the
coherent phonon effects in 2D and demonstrates the potential of using coherent
phonon effects to significantly modify thermal transport of 2D materials
without making drastic changes to their fundamental compositions.
