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Recent NMR experiments by Singer et al. [Singer et al. Phys. Rev. Lett. 95,236403 (2005).] showed a deviation from Fermi-liquid behavior in carbonnanotubes with an energy gap evident at low temperatures. Here, a comprehensivetheory for the magnetic field and temperature dependent NMR 13C spin-latticerelaxation is given in the framework of the Tomonaga-Luttinger liquid. The lowtemperature properties are governed by a gapped relaxation due to a spin gap (~30K), which crosses over smoothly to the Luttinger liquid behaviour withincreasing temperature.

Spin gap and Luttinger liquid description of the NMR relaxation in carbon nanotubes