Theoretical description of thermal transport in graphene: The issues of phonon cut-off frequencies and polarization branches

We discuss theoretical approaches for description of the phonon thermal transport in graphene and identify open questions and problems. Specifically, we show that due to a fundamental ambiguity in the definition of the intrinsic thermal conductivity of two-dimensional (2-D) systems the calculations that use an arbitrary low-bound cut-off for the phonon frequency in the thermal conductivity integral lead to erroneous results. The problem of the relative contributions of the longitudinal acoustic (LA), transverse acoustic (TA), and out-of-plane phonon polarization branches to thermal transport in graphene is also discussed. Theoretical thermal conductivity data for graphene, obtained by different approaches, are compared with those for carbon nanotubes.