Phonon dispersion of carbon nanotubes

We present the phonon dispersion relations of single-wall carbon nanotubes calculated within a force-constants approach. By using the full symmetry group of the tubes, we are able to calculate the dispersion relations for any chirality starting from one single carbon atom. We find an overbending in the highest optical branch between 6 and 12 cm⁻¹ independent of the tube diameter. The order of the high-energy modes at the Γ-point differs from the results derived from simple zone folding. The splitting between the two Raman active optical modes with A₁ symmetry at the Γ-point of chiral tubes is ≈4 cm⁻¹ for typical diameters; it increases with decreasing tube diameter.     

Phonon spectrum of double-wall carbon nanotubes

The results of studying the phonon spectra of carbon nanotubes within the framework of the periodic-cluster model are presented. Special attention is paid to the phonon spectrum of double-wall nanotubes. It is shown that the spectrum is separated into two subbands corresponding to the acoustic and optical vibrational modes. A specific feature of the phonon dispersion curves is their “doublet” character. The spectrum has an acoustic mode corresponding to longitudinal oscillations of the two walls of a double-wall carbon nanotube with respect to each other.     

单壁纳米碳管的声子谱研究

通过五步旋转操作方便地得到了不同位置原子间的力常数矩阵，从而可以使对各种不同类型管的声子谱的计算变得简便. 计算表明，非螺旋的扶手椅型（n, n）管与锯齿型(n, 0)管的非简并和二重简并模式数分别为12和6(n-1)，这与从群论等方法所得结果相符. 关键词： 纳米碳管 声子谱 振动模式密度 动力学矩阵     

Humidity effect on the interaction between carbon nanotubes and graphite

An atomic force microscope is used to study the effect of humidity on the interaction between carbon nanotubes anchored to atomic force microscopy tips and various samples. Commercial silicon tips were also used for comparison. Adhesion force and dissipative energy were measured between these tips and highly oriented pyrolytic graphite (HOPG) and PMMA in contact mode. The data provides a detailed understanding of carbon nanotube interactions as a function of humidity.     

Phonon dispersions in graphene sheet and single-walled carbon nanotubes

In the present research paper, phonons in graphene sheet have been calculated by constructing a dynamical matrix using the force constants derived from the second-generation reactive empirical bond order potential by Brenner and co-workers. Our results are comparable to inelastic X-ray scattering as well as first principle calculations. At Γ point, for graphene, the optical modes (degenerate) lie near 1685 cm^???1. The frequency regimes are easily distinguishable. The low-frequency (ω→ 0) modes are derived from acoustic branches of the sheet. The radial modes can be identified with ω→ 584 cm^???1. High-frequency regime is above 1200 cm^???1 (i.e. ZO mode) and consists of TO and LO modes. The phonons in a nanotube can be derived from zone folding method using phonons of a single layer of the hexagonal sheet. The present work aims to explore the agreement between theory and experiment. A better knowledge of the phonon dispersion of graphene is highly desirable to model and understand the properties of carbon nanotubes. The development and production of carbon nanotubes (CNTs) for possible applications need reliable and quick analytical characterization. Our results may serve as an accurate tool for the spectroscopic determination of the tube radii and chiralities.     

Phonon density of states of single-wall carbon nanotubes

The vibrational density of states of single-wall carbon nanotubes (SWNT) was obtained from inelastic neutron scattering data from 0 to 225 meV. The spectrum is similar to that of graphite above 40 meV, while intratube features are clearly observed at 22 and 36 meV. An unusual energy dependence below 10 meV is assigned to contributions from intertube modes in the 2D triangular lattice of SWNT bundles, and from intertube coupling to intratube excitations. Good agreement between experiment and a calculated density of states for the SWNT lattice is found over the entire energy range.     

Phonon dispersion in graphite

We measured the dispersion of the graphite optical phonons in the in-plane Brillouin zone by inelastic x-ray scattering. The longitudinal and transverse optical branches cross along the Gamma-K as well as the Gamma-M direction. The dispersion of the optical phonons was, in general, stronger than expected from the literature. At the K point the transverse optical mode has a minimum and is only approximately 70 cm(-1) higher in frequency than the longitudinal mode. We show that first-principles calculations describe very well the vibrational properties of graphene once the long-range character of the dynamical matrix is taken into account.     

Majorana zero modes in graphene with trigonal warping

We study the low energy properties of warped monolayer graphene, where the symmetry of the original honeycomb lattice reveals itself. The zero energy solutions are Majorana fermions, whose wave function, originating from the corresponding modified Dirac equation is spatially localized. Experimental consequences are discussed. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phonon and electronic nonradiative decay mechanisms of excitons in carbon nanotubes

We investigate theoretically the rates of nonradiative decay of excited semiconducting nanotubes by a variety of decay mechanisms and compare them with experimental findings. We find that the multiphonon decay (MPD) of free excitons is too slow to be responsible for the experimentally observed lifetimes. However, MPD lifetimes of localized excitons could be 2-3 orders of magnitude shorter. We also propose a new decay mechanism that relies on a finite doping of nanotubes and involves exciton decay into an optical phonon and an intraband electron-hole pair. The resulting lifetime is in the range of 5 to 100 ps, even for a moderate doping level.     

Phonon and thermal properties of achiral single wall carbon nanotubes

A detailed theoretical study of the phonon and thermal properties of achiral single wall carbon nanotubes has been carried out using force constant model considering up to third nearest-neighbor interactions. We have calculated the phonon dispersions, density of states, radial breathing modes (RBM) and the specific heats for various zigzag and armchair nanotubes, with radii ranging from 2.8 Å to 11.0 Å. A comparative study of phonon spectrum with measured Raman data reveals that the number of Raman active modes for a tube does not depend on the number of atoms present in the unit cell but on its chirality. Calculated phonon modes at the zone center more or less accurately predicted the Raman active modes. The radial breathing mode is of particular interest as for a specific radius of a nanotube it is found to be independent of its chirality. We have also calculated the variation of RBM and G-band modes for tubes of different radii. RBM shows an inverse dependence on the radius of the tube. Finally, the values of specific heat are calculated for various nanotubes at room temperature and it was found that the specific heat shows an exponential dependence on the diameter of the tube.     

单壁碳纳米扶手椅、锯齿管声子色散关系的计算

引用石墨经验力常数计算碳纳米管声子色散关系时，必须处理由二维平面卷曲形成三维实体纳米管所引入的问题. 报道对一系列扶手椅和锯齿单壁碳纳米管计及卷曲效应的声子色散关系的计算结果. 基于实际的数值计算结果，以及对单壁碳纳米扶手椅、锯齿管结构的对称性分析，讨论了Brillouin区中心Γ点晶格振动模的分类. 关键词： 碳纳米管 声子色散关系     

Chemisorption of atomic hydrogen in graphite and carbon nanotubes

An orthogonal tight-binding model of the carbon-hydrogen interaction was modified to deal with the different hybridization states of atomic hydrogen on carbon surfaces, without explicitly including charge self-consistency. The resulting model has great flexibility and computational efficiency, generally with a good quantitative accuracy. The non-self-consistent C-H model was tested by calculating structural properties of small hydrocarbons and simple polymers, and against ab initio results of H binding to both perfect and defective graphite. The model was employed to study the chemisorption properties and dynamics of atomic hydrogen on perfect and defective surfaces of graphite and carbon nanotubes.     

Optical absorption of graphite and single-wall carbon nanotubes

A review of the electronic dipole transitions in graphite and single-wall carbon nanotubes is presented. Because of its singular electronic structure, the optical absorption matrix element as a function of wave vector has a node in the two-dimensional Brillouin zone of graphite, which depends linearly on the optical polarization direction. In the case of the single-wall carbon nanotubes, the dipole selection rule and the van Hove singularity in the joint density of states will give a characteristic behavior, which is observed by luminescence and resonance Raman spectroscopy. PACS 78.30.Na; 78.20.Bh; 78.66.Tr; 63.22.+m; 36.20.Kd; 36.20.Ng     

Phonon anharmonicities in graphite and graphene

We determine from first principles the finite-temperature properties-linewidths, line shifts, and lifetimes-of the key vibrational modes that dominate inelastic losses in graphitic materials. In graphite, the phonon linewidth of the Raman-active E(2g) mode is found to decrease with temperature; such anomalous behavior is driven entirely by electron-phonon interactions, and does not appear in the nearly degenerate infrared-active E(1u) mode. In graphene, the phonon anharmonic lifetimes and decay channels of the A(1)' mode at K dominate over E(2g) at Gamma and couple strongly with acoustic phonons, highlighting how ballistic transport in carbon-based interconnects requires careful engineering of phonon decays and thermalization.     

Phonon dispersion relations and soft modes of 4 carbon nanotubes

The phonon dispersion relations of three kinds of 4 carbon nanotubes are calculated by using the density functional perturbation theory. It is found that the frequencies of some phonon modes are very sensitive to the smearing width used in the calculations, and eventually become negative at low electronic temperature. Moreover, two kinds of soft modes are identified for the (5,0) tube which are quite different from those reported previously. Our results suggest that the (5,0) tube remains metallic at very low temperature, instead of the metallic-semiconducting transition claimed before.     

Interaction of C60 with carbon nanotubes and graphite

The interaction of C60 with single-wall carbon nanotubes (SWNTs) and graphite is studied experimentally by thermal desorption spectroscopy and theoretically by molecular-mechanics and molecular-dynamics calculations. The van der Waals parameters and force field for C60-graphene and C60-SWNT interactions are derived from the low-coverage C60 binding energy to the graphite surface. We use these to compare the efficiency of different mechanisms by which C60 can be encapsulated into SWNTs.     

Phonon softening in individual metallic carbon nanotubes due to the Kohn Anomaly

We have studied the line shape and frequency of the G band Raman modes in individual metallic single walled carbon nanotubes (M-SWNTs) as a function of Fermi level (epsilonF) position, by tuning a polymer electrolyte gate. Our study focuses on the data from M-SWNTs where explicit assignment of the G- and G+ peaks can be made. The frequency and line shape of the G- peak in the Raman spectrum of M-SWNTs is very sensitive to the position of the Fermi level. Within +/- variant Planck's over 2piomega/2 (where variant Planck's over 2piomega is the phonon energy) around the band crossing point, the G- mode is softened and broadened. In contrast, as the Fermi level is tuned away from the band crossing point, a semiconductinglike G band line shape is recovered both in terms of frequency and linewidth. Our results confirm the predicted softening of the A-symmetry LO phonon mode frequency due to a Kohn anomaly in M-SWNTs.     

Piezoresistive effect in single-walled carbon nanotubes

This paper reports on the results of the theoretical investigation of the piezoresistive effect in single-walled carbon nanotubes of two structural modifications: arm-chair type and zig-zag type. The variation in the band gap of semiconducting nanotubes under the influence of the compressive and tensile deformations has been analyzed. The main quantitative characteristic of the piezoresistive effect—the longitudinal component of the elastic conductivity tensor—has been calculated, and its dependence on the diameter of semiconducting nanotubes has been shown. The variants of practical implementation of the effect under study have been proposed.     

Electron diffraction on graphite nanocrystals in the walls of carbon nanotubes

The structure and defects in the walls and cavities of carbon nanotubes were examined by electron diffraction, transmission electron microscopy, energy dispersive X-ray analysis and Raman spectroscopy. The predominating defects in the walls of the nanotubes are graphite nanocrystals having a preferential orientation in the direction of the nanotube axis, and another significant type of defects are particles of the catalyst in the nanotube cavities. In the cavities, also the presence of molybdenum was proved having its origin in the catalyst.