Journal
PHYSICAL REVIEW B
Volume 66, Issue 15, Pages -Publisher
AMERICAN PHYSICAL SOC
DOI: 10.1103/PhysRevB.66.153408
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The low-temperature specific heat of single-walled carbon nanotubes (isolated and bundled) and multiwalled carbon nanotubes is calculated within force-constant dynamical models. It is shown that, due to the quadratic dependence of the frequency omega of the transverse-acoustic phonons on the wave number q, the phonon density of states has a singularity of the type 1/rootomega and the very low-temperature specific heat varies as rootT with the temperature T. With the increase of the diameter of the system, the contributions of the longitudinal- and torsional-acoustic phonons to the specific heat begin to prevail and the latter becomes linear in T. These results are confirmed by the recent experimental data.
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