We have measured a strictly linear π plasmon dispersion along the axis of individualized single wall carbon nanotubes, which is completely different from plasmon dispersions of graphite or bundled single wall carbon nanotubes. Comparative ab initio studies on graphene based systems allow us to reproduce the different dispersions. This suggests that individualized nanotubes provide viable experimental access to collective electronic excitations of graphene, and it validates the use of graphene to understand electronic excitations of carbon nanotubes. In particular, the calculations reveal that local field effects (LFE) cause a mixing of electronic transitions, including the 'Dirac cone', resulting in the observed linear dispersion. PACS numbers: 73.20.Mf,78.20.Bh Single-wall carbon nanotubes (SWNT) and its parent compound graphene are archetypes of low dimensional systems with strongly anisotropic and unique electronic properties which make them interesting for both fundamental research and as building blocks in nanoelectronic applications [1]. Their electronic bandstructure is frequently studied. In graphene, the linear band dispersion at the Fermi level, the 'Dirac cone', leads to unique characteristics in nanoelectronic devices [2]. One can expect a strong analogy between graphene and isolated SWNT for excitations along the sheet and along the tube axis, respectively. Within the zone-folding model, i.e. neglecting curvature effects, the graphene bandstructure is sliced along parallel lines when the sheet is rolled up into a cylinder. The result are characteristic van Hove singularities (VHS) in the density of states (DOS) [3]. Bulk (i.e. bundled) SWNT show an optical absorption peak at ∼ 4.5 eV due to transitions of the π electrons [4]. In vertically aligned SWNT (VA-SWNT) one finds the same peak position for onaxis polarization and an additional peak for perpendicular polarization at ∼ 5.2 eV [5]. Further information can be obtained from collective electronic excitations (plasmons) beyond the optical limit [6] (i.e. momentum transfer q > 0). Angle resolved electron energy loss spectroscopy (EELS) assesses the detailed plasmon dispersion [7,8], but it is so far missing for freestanding isolated sp 2 carbon systems. Models based on the homogeneous electron gas [9], or the tight-binding scheme [10,11] have been used to describe these excitations. The former are however bound to metallic systems. The latter have provided valuable insight and predictions for the properties of isolated sheets, tubes, and assemblies of these objects; in particular, they have predicted an almost linear plasmon dispersion for isolated systems. However, the tight binding results neglect screening beyond the π bands, and they depend on parameters that hide the underlying complexity. No realistic parameter-free calculations have been performed to predict the plasmon dispersion in these systems, nor has its origin been analyzed. Instead, ab initio spectroscopy calculations have dealt with absorption spectra (q → 0) for SWNT [12,13,14],...
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.
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.
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