Theoretical evidence for T1/2 specific heat behavior in carbon nanotube systems Original Research Article

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 ω of the transverse acoustic phonons on the wavenumber q the phonon density of states has a singularity of the type ω−1/2 and the very low-temperature specific heat varies as T1/2 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 recent experimental data.