  The thermal properties of graphitic ribbon are investigated based on
Brenner's empirical potential. The reliability and usefulness of the empirical
potential to address the thermal properties of covalent-bonded carbon
nanostructures are verified through a comparison of phonon dispersion relations
and the density of states of carbon nanotubes with first-principles
calculations. The analysis reveals unique edge-phonon states that are highly
localized at edge carbon atoms of both armchair and zigzag ribbons. Applying
the phonon dispersion relations to the Landauer formula of phonon transport,
the quantization and universal features of the low-temperature thermal
conductance of graphitic ribbon are elucidated, and it is found that the width
of the quantization plateau in the low-temperature region is inversely
proportional to the ribbon width.
