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

TL;DR

This paper develops a comprehensive theoretical model for NMR relaxation in carbon nanotubes, explaining the crossover from gapped spin-liquid behavior at low temperatures to Luttinger liquid behavior at higher temperatures.

Contribution

It introduces a unified theory combining spin gap and Luttinger liquid descriptions to explain NMR relaxation phenomena in carbon nanotubes.

Findings

Identification of a spin gap of approximately 30K affecting relaxation.

Smooth crossover from gapped behavior to Luttinger liquid behavior with increasing temperature.

Agreement with experimental NMR relaxation data.

Abstract

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