  First-principles density-functional calculations are performed to investigate
the thermal transport properties in graphene nanoribbons (GNRs). The
dimensional crossover of thermal conductance from one to two dimensions (2D) is
clearly demonstrated with increasing ribbon width. The thermal conductance of
GNRs in a few nanometer width already exhibits an approximate low-temperature
dependence of $T^{1.5}$, like that of 2D graphene sheet which is attributed to
the quadratic nature of dispersion relation for the out-of-plane acoustic
phonon modes. Using a zone-folding method, we heuristically derive the
dimensional crossover of thermal conductance with the increase of ribbon width.
Combining our calculations with the experimental phonon mean-free path, some
typical values of thermal conductivity at room temperature are estimated for
GNRs and for 2D graphene sheet, respectively. Our findings clarify the issue of
low-temperature dependence of thermal transport in GNRs and suggest a
calibration range of thermal conductivity for experimental measurements in
graphene-based materials.
