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.     

Third and fourth optical transitions in semiconducting carbon nanotubes

We have studied the optical transition energies of single-wall carbon nanotubes over broad diameter (0.7-2.3 nm) and energy (1.26-2.71 eV) ranges, using their radial breathing mode Raman spectra. We establish the diameter and chiral angle dependence of the poorly studied third and fourth optical transitions in semiconducting tubes. Comparative analysis between the higher lying transitions and the first and second transitions show two different diameter scalings. Quantum mechanical calculations explain the result showing strongly bound excitons in the first and second transitions and a delocalized electron wave function in the third transition.     

Third-order nonlinear optical response in double-walled carbon nanotubes

Resonant behavior and magnitudes of third-order nonlinear optical susceptibilities in double-walled carbon nanotubes (DWNTs) have been investigated by means of femtosecond pump-probe spectroscopy with different pump-photon energies. With the selective excitation of the E₂₂ exciton transition of the inner tubes labeled by the chiral vector indices (7,5) and (7,6), the imaginary part of nonlinear susceptibility Imχ⁽³⁾ has shown the resonant enhancement compared with the case of the nonresonant excitation of the specific tube. The nonlinear response signal at the E₂₂ transition energy of the (8,7) tube has been also enhanced for the excitation of the G-band phonon sideband of its E₂₂ transition. This result is consistent with the phonon-mediated nonlinear optical process observed for the E₂₂ transitions in single-walled carbon nanotubes (SWNTs). It has been also found that the values of the figure of merit Im χ⁽³⁾/α (α: absorption coefficient) of the inner tubes in DWNTs are smaller than those of the corresponding SWNTs, which is interpreted in terms of decay time shortening due to the energy relaxation between the inner and outer tubes.     

Ultrafast dynamics of delocalized and localized electrons in carbon nanotubes

We report on the dynamics of the dielectric function of single-wall carbon nanotubes in the 10-30 THz frequency range after ultrafast laser excitation. The absence of a distinct free-carrier response is attributed to the photogeneration of strongly bound excitons in the tubes with large energy gaps. We find a feature of enhanced transmission caused by the blocking of optical transitions in small-gap tubes. The rapid decay of a featureless background with pronounced dichroism is associated with the increased absorption of spatially localized charge carriers before thermalization is completed.     

Optical transitions in single-wall boron nitride nanotubes

Optical transitions in single-wall boron nitride nanotubes are investigated by means of optical absorption spectroscopy. Three absorption lines are observed. Two of them (at 4.45 and 5.5 eV) result from the quantification involved by the rolling up of the hexagonal boron nitride (h-BN) sheet. The nature of these lines is discussed, and two interpretations are proposed. A comparison with single-wall carbon nanotubes leads one to interpret these lines as transitions between pairs of van Hove singularities in the one-dimensional density of states of boron nitride single-wall nanotubes. But the confinement energy due to the rolling up of the h-BN sheet cannot explain a gap width of the boron nitride nanotubes below the h-BN gap. The low energy line is then attributed to the existence of a Frenkel exciton with a binding energy in the 1 eV range.     

Excitons in optical spectra of boron-nitride (BN) nanotubes

Exciton effects are studied in single-wall boron-nitride nanotubes. The Coulomb interaction dependence of the band gap, the optical gap, and the binding energy of excitons are discussed. The optical gap of the (5,0) nanotube is about 6 eV at the on-site interaction U=2t with the hopping integral t=1.1 eV. The binding energy of the exciton is 0.50 eV for these parameters. This energy agrees well with that of other theoretical investigations. We find that the energy gap and the binding energy are almost independent of the geometries of nanotubes. This novel property is in contrast with that of the carbon nanotubes, which show metallic and semiconducting properties depending on the chiralities.     

Photorefractive polymer composites for the IR region based on carbon nanotubes

The photorefractive properties of polymer composites based on aromatic polyimide and single-wall carbon nanotubes are studied using radiation at a wavelength of 1064 nm. It is found that the nanotubes possess photoelectric sensitivity in this spectral region and that the kinetic photorefractive characteristics of the polymer composites are entirely determined by the photogeneration and charge transport characteristics of the layers. The two-beam gain coefficient of the signal beam measured for a composite consisting of aromatic polyimide and 0.25 wt % of single-wall carbon nanotubes in a constant electric field E₀ = 79 V/μm is equal to 84 cm^?1 and exceeds the optical absorption coefficient by 59 cm^?1. The refractive index modulation is equal to Δn = 0.004 at E₀ = 54 V/μm.     

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     

Optical Kerr effect exhibited by carbon nanotubes and carbon/metal nanohybrid materials

Structural modification of carbon nanotubes in combination with metallic nanoparticles is reported. An enhancement in the nonlinear optical refraction of multi-wall carbon nanotubes by the incorporation of platinum nanoparticles was observed. Comparative results were analyzed taking into account the participation of single-wall carbon nanotubes that originate a decrease in the nonlinear optical response of the multi-wall carbon nanotubes integrating a thin film. A Nd:YAG laser system featuring 532 nm wavelength with 4 ns pulse duration in a two-wave mixing experiment was employed for exploring the studied optical nonlinearities of the samples. The contribution of optical processes to mechanical characteristics dependent on high optical irradiance in carbon nanotubes was described. A variation in the mass density associated to the optically irradiated tubes allowed us to calculate the change in Young's modulus in a thin film configuration. The estimation of an opto-mechanical phenomenon was based on the evaluation of the nonlinearity of index responsible for the optical Kerr effect. According to Raman and optical evaluations, the inclusion of metallic nanoparticles in carbon structures results in a modification of surface that also gives origin to noticeable optical Kerr nonlinearities. Potential applications for developing laser-induced controlled opto-mechanical nanohybrid systems can be contemplated.     

Carbon systems of polymerized nanotubes: Crystal and electronic structures

Molecular dynamic calculations are carried out for the (P, T) phase diagram of a covalent compound of cross-linked carbon single-wall nanotubes (SWNT) and for the structures and electronic spectra of the novel crystals of polymerized carbon nanotubes. It is shown that the transformation of covalently bonded nanotubes in a close-packed conducting structure cardinally modifies their electronic properties. The P-SWNT crystal becomes semiconducting and, upon complete transformation of sp ²-hybridized carbon atoms into sp ³-hybridized ones, it becomes an insulator.     

单壁碳纳米管力学行为的数字散斑相关法实验研究

通过直接单向拉伸超长单壁碳纳米管束长绳,首次借助高精度数字散斑相关法,并结合显维放大技术,测量了单壁碳纳米管的弹性模量和拉伸强度。试验中观察了单壁碳纳米管束长绳的断裂过程。单壁碳纳米管束长绳通过改进的化学气相沉积技术生成。试验得到单壁碳纳米管的平均杨氏模量为129.0±70.3GPa,平均拉伸强度为1.95±0.56GPa,低于计算值和先前其它文献的试验值。     

Ultrafast carrier dynamics in single-wall carbon nanotubes

Time-resolved carrier dynamics in single-wall carbon nanotubes is investigated by means of two-color pump-probe experiments. The recombination dynamics is monitored by probing the transient photobleaching observed on the interband transitions of the semiconducting tubes. This dynamics takes place on a 1 ps time scale which is 1 order of magnitude slower than in graphite. Transient photoinduced absorption is observed for nonresonant probing and is interpreted as a global redshift of the pi-plasmon resonance. We show that the opening of the band gap in semiconducting carbon nanotubes determines the nonlinear response dynamics over the whole visible and near-infrared spectrum.     

Strong effects of substitute nitrogen-doping on linear optical absorption spectra of zigzag carbon nanotubes

We theoretically study effects of substitute nitrogen-doping on linear optical properties of zigzag carbon nanotubes using tight-binding model and gradient approximation. It is found that, generally, nitrogen-doping reduces the value of absorption peaks and creates a number of new absorption peaks. In addition, near the low energy range, linear optical absorption spectra of nitrogen-doped (m,0) zigzag tubes are remarkably dependent on whether m mod 3 (the remainder of dividing m by 3) is equal to 0, 1 or 2.     

Second-and third-harmonic generation by carbon nanotubes irradiated with femtosecond laser pulses

Femtosecond pulses of a Cr:forsterite laser are used to study second-and third-harmonic generation in a layer of single-wall carbon nanotubes produced by low-velocity spraying. The harmonic amplitude in our experiments scales as (I _p)ⁿ as a function of the pump intensity I _p, with n=2 and 3 for the second and third harmonics, respectively. This scaling law holds up to pump intensities on the order of 10¹²W/cm². The ratio of the maximum signal to the averaged background in the spectra of the second and third harmonics is estimated as 50 and 30, respectively. The second and third harmonics produced by a linearly polarized pump field are also linearly polarized, with their polarization vectors oriented along the polarization direction of the pump field. The capabilities of nonlinear-optical methods for structural and morphological analysis of carbon nanotubes are discussed, as well as ways to create solid-state carbon-nanotube generators of optical harmonic.     

Optical studies of carbon nanotubes and nanographites

Resonance Raman and photoluminescence excitation (PLE) spectroscopies are used to study the optical properties of different types of carbon nanostructures such as carbon nanotube, nanoribbons, nanographites and graphite edges. In the resonance Raman experiments of carbon nanotubes, the (n,m) assignment is obtained by comparing the experimental and theoretical diameter and chirality dependence of the optical transitions. The influence of the environment on the optical transitions of the nanotubes is also obtained in the Raman experiments. The PLE measurements in different samples of carbon nanotubes show both direct and phonon-assisted optical transitions, and the results give new evidences that the optical transitions in nanotubes have an excitonic character, which is very strong for the low energy transitions. We also analyze the Raman spectra of nanoribbons and nanographites, showing that this technique is an important tool for defect characterization in graphitic materials, and can be used to distinguish the atomic structure of the graphite edges.     

Optical properties of semiconducting carbon nanotubes under axial magnetic field

The linear polarizability absorption spectra of semiconducting carbon nanotubes under axial magnetic field (B) have been calculated by the π-orbital tight-binding model and sum-over-state method. We have found that the optical spectra are split by the B-induced symmetry breaking and the amount of splitting increases with increase of magnetic field. Although the results are obtained within the noninteracting tight-binding model, the amount of splitting is still consistent with the experimental observation, offering a fast estimation of the B-induced splitting. Our numerical results also indicate that the splitting amounts of the second and third absorption peaks are close to that of the first one, which may be observed by the future experiments.     

Interaction of oxygen with 4 ? carbon nanotubes

We review our density functional study of oxygen adsorption on the outer surface of 4 ? single-wall carbon nanotubes, which have been recently synthesized using a templating method. The stability of these 4 ? tubes under ambient conditions is investigated by the nudged elastic band technique and further confirmed by the experimentally measured Raman spectra. Different adsorption pictures of singlet O₂ could be used to select a single chirality from a mixture of these ultra-small radius tubes.      

Electronic structure and dynamics of optically excited single-wall carbon nanotubes

We have studied the electronic structure and charge-carrier dynamics of individual single-wall carbon nanotubes (SWNTs) and nanotube ropes using optical and electron–spectroscopic techniques. The electronic structure of semiconducting SWNTs in the band-gap region is analyzed using near-infrared absorption spectroscopy. A semi-empirical expression for E₁₁^S transition energies, based on tight-binding calculations is found to give striking agreement with experimental data. Time-resolved PL from dispersed SWNT-micelles shows a decay with a time constant of about 15 ps. Using time-resolved photoemission we also find that the electron–phonon (e–ph) coupling in metallic tubes is characterized by a very small e–ph mass-enhancement of 0.0004. Ultrafast electron–electron scattering of photo-excited carriers in nanotube ropes is finally found to lead to internal thermalization of the electronic system within about 200 fs. PACS 78.47.+p; 81.07.De; 78.67.Ch; 87.64.Ni