Low-temperature specific heat of single-wall carbon nanotubes

Previous low-temperature heat capacity measurements down to 2 K have been analyzed as resulting from one-dimensional quantum confinement of single-wall carbon nanotube (SWNT) vibrational modes [J. Hone et al., Science 289, 1730 (2000)]. We extended the measurements on SWNT ropes from the same preparation technique down to 0.1 K. The specific heat shows three contributions: a well-defined $T^{-2}$ term from nuclear hyperfine interactions in ferromagnetic impurities and a monotonously varying vibrational contribution very sensitive to adsorbed gases, in particular ${}^4\mathrm{He}.$ In the best outgassing conditions, the specific heat yields the $T^3$ term originating from intertube coupling, in agreement with J. Hone et al. [Science 289, 1730 (2000)]. The third contribution follows sublinear, power-law T dependence. We discuss our results in relation to inelastic neutron scattering experiments.