Enhanced NMR relaxation of Tomonaga-Luttinger liquids and the magnitude of the carbon hyperfine coupling in single-wall carbon nanotubes.

Recent transport measurements [Churchill et al. Nature Phys. 5, 321 (2009)] found a surprisingly large, 2-3 orders of magnitude larger than usual (13)C hyperfine coupling (HFC) in (13)C enriched single-wall carbon nanotubes. We formulate the theory of the nuclear relaxation time in the framework of the Tomonaga-Luttinger liquid theory to enable the determination of the HFC from recent data by Ihara et al. [Europhys. Lett. 90, 17,004 (2010)]. Though we find that 1/T(1) is orders of magnitude enhanced with respect to a Fermi-liquid behavior, the HFC has its usual, small value. Then, we reexamine the theoretical description used to extract the HFC from transport experiments and show that similar features could be obtained with HFC-independent system parameters.

Electron spin resonance signal of Luttinger liquids and single-wall carbon nanotubes.

A comprehensive theory of electron spin resonance (ESR) for a Luttinger liquid state of correlated metals is presented. The ESR measurables such as the signal intensity and the linewidth are calculated in the framework of Luttinger liquid theory with broken spin rotational symmetry as a function of magnetic field and temperature. We obtain a significant temperature dependent homogeneous line broadening which is related to the spin-symmetry breaking and the electron-electron interaction. The result crosses over smoothly to the ESR of itinerant electrons in the noninteracting limit. These findings explain the absence of the long-sought ESR signal of itinerant electrons in single-wall carbon nanotubes when considering realistic experimental conditions.

Isotope engineering of carbon nanotube systems.

The synthesis of a unique isotope engineered system, double-wall carbon nanotubes with natural carbon outer and highly 13C enriched inner walls, is reported from isotope enriched fullerenes encapsulated in single-wall carbon nanotubes (SWCNTs). The material allows the observation of the D line of the highly defect-free inner tubes that can be related to a curvature induced enhancement of the electron-phonon coupling. Ab initio calculations explain the inhomogeneous broadening of inner tube Raman modes due to the distribution of different isotopes. Nuclear magnetic resonance shows a significant contrast of the isotope enriched inner SWCNTs compared to other carbon phases and provides a macroscopic measure of the inner tube mass content. The high curvature of the small diameter inner tubes manifests in an increased distribution of the chemical shift tensor components.

Unusual high degree of unperturbed environment in the interior of single-wall carbon nanotubes.

Double wall carbon nanotubes were prepared by vacuum annealing of single wall carbon nanotubes filled with C60. Strong evidence is provided for a highly defect free and unperturbed environment in the interior of the tubes. This is concluded from unusual narrow Raman lines for the radial breathing mode of the inner tubes. Lorentzian linewidths scale down to 0.35 cm(-1) which is almost 10 times smaller than linewidths reported so far for this mode. A splitting is observed for the majority of the Raman lines. It is considered to originate from tube-tube interaction between one inner tube and several different outer tubes. The highest RBM frequency detected is 484 cm(-1) corresponding to a tube diameter of only 0.50 nm. Labeling of the Raman lines with the folding vector is provided for all inner tubes. This labeling is supported by density functional calculations.

Origin of the fine structure of the Raman D band in single-wall carbon nanotubes.

Experiments show that the D bands of bundles of single wall carbon nanotubes have a fine structure, apparently consisting of more than one subband. Using the double resonance theory, we calculate for the first time the D band for a sample of a given diameter distribution for seven different laser excitation energies in a wide range. In addition, a detailed theoretical explanation for the fine structure of the D band is provided. The calculated results agree well with experiments and show that the main factors in determining the fine structure are an enhanced trigonal warping of the phonon dispersion, the presence of a diameter distribution in the sample, and--most importantly--the resonance from the Van Hove singularities.

Periodic resonance excitation and intertube interaction from quasicontinuous distributed helicities in single-wall carbon nanotubes

Photoselective resonance Raman scattering from laser ablation grown single-wall carbon nanotubes is demonstrated to be consistent with a response from tubes with all geometrically allowed helicities. This information is drawn from an analysis of the resonance scattering by combining ab initio calculations for the mode frequencies with evaluations of the resonance cross sections for isolated tubes. The resonance excitation was found to exhibit an oscillatory behavior. To match the experiments and the calculations, the frequencies obtained from the latter must be up-shifted by 8.5% on the average. This stiffening is ascribed to the tube-tube interaction in the carbon nanotube bundles.