[show abstract][hide abstract] ABSTRACT: The D band Raman intensity is calculated for armchair edged graphene nanoribbons using an extended tight-binding method in which the effect of interactions up to the seventh nearest neighbor is taken into account. The possibility of a double resonance Raman process with multiple scattering events is considered by calculating a T matrix through a direct diagonalization of the nanoribbon Hamiltonian. We show that long-range interactions play an important role in the evaluation of both the D band intensity and that the main effect of multiple scattering events on the calculated D band is an overall increase in intensity by a factor of 4. The D band intensity is shown to be independent of the nanoribbon widths for widths larger than 17 nm, leading to the well-known linear dependence of the ID/IG ratio on the inverse of the crystalline size. The D band intensity was shown to be nearly independent of the laser excitation energy and to have a maximum value for incident and scattering photons polarized along the direction of the edge.
Physical Review B 01/2011; 83(24). · 3.77 Impact Factor
[show abstract][hide abstract] ABSTRACT: High resolution far infrared absorption measurements were carried out for single walled and double walled carbon nanotubes samples (SWCNT and DWCNT) encased in a polyethylene matrix to investigate the temperature and bundling effects on the low frequency phonons associated with the low frequency circumferential vibrations. At a temperature where kBT is significantly lower than the phonon energy, the broad absorption features as observed at room temperature become well resolved phonon transitions. For a DWCNT sample whose inner tubes have a similar diameter distribution as the SWCNT sample studied, a series of sharp features were observed at room temperature at similar positions as for the SWCNT samples studied. The narrow linewidth is attributed to the fact that the inner tubes are isolated from the polyethylene matrix and the weak inter-tubule interactions. More systematic studies will be required to better understand the effects of inhomogeneous broadening and thermal-excitation on the detailed position and lineshape of the low frequency phonon features in carbon nanotubes.
[show abstract][hide abstract] ABSTRACT: In this work we investigate the presence of a torsional instability in single-wall carbon nanotubes which causes small diameter chiral carbon nanotubes to show natural torsion. To obtain insight into the nature of this instability, the natural torsion is calculated using an extended tight-binding model and is found to decrease as the inverse cube of the diameter. The dependence of the natural torsion on chiral angle is found to be different for metallic and semiconducting nanotubes, specially for near-armchair nanotubes, for which the behavior of semiconducting nanotubes deviates from the simple sin6 behavior observed for metallic nanotubes. The presence of this natural torsion implies a revision of the calculation of the chiral angle of the nanotubes. Several theoretical and experimental studies indicate that the electronic and optical properties of carbon nanotubes are extremely sensitive to structural deformations, such as axial, radial, or torsional strains. 1–4 Due to the possible applicabil-ity of nanotubes for electromechanical actuators, the tor-sional properties of multiwall and single-wall carbon nano-tubes SWNTs have been widely investigated both experimentally and theoretically. 4–10 However, for the inter-pretation of these works, these reports assume that in their natural state, carbon nanotubes are free from such geometri-cal deformations. In the case of radial and axial strains, this assumption can always be asserted since these deformations maintain the full symmetry of the nanotube and thus the nanotube structure can be renormalized to the new param-eters without losing its basic properties. However, in the case of a torsional strain, the pure translational symmetry of the nanotube is broken and thus the usual symmetry representa-tion of the nanotube unit cell needs to be revised. One of the main problems involved in the simulation of nanotube properties under torsion is the fact that the appli-cation of a torsional stress to the carbon nanotube breaks the pure translational symmetry of the nanotube unit cell. For this reason, calculations involving the effects of torsion are done either on finite-length nanotubes or in supercells. How-ever, these studies were able to obtain important information about the mechanical properties of nanotubes. One interest-ing result was reported by Liang et al., 9 which showed that the relationship between the axial-strain-induced torsion in chiral nanotubes is asymmetric with respect to zero strain. On the other hand, Chang et al. 10 showed also that the effects of torsion on a chiral single-wall carbon nanotube is depen-dent on the load direction. These results originate from the fact that chiral nanotubes do not have inversion symmetry and thus the effects of a torsional stress in one direction of a nanotube is different from that in another direction. This fact brings up several different questions, one of which is about the effect of this asymmetry on the nanotube structure itself. In the present work we investigate the presence of a natu-ral torsion in chiral single-wall carbon nanotubes by using a symmetry-adapted tight-binding calculation. The presence of this natural torsion is explained in terms of a torsional insta-bility similar to the Peierls instability expected for metallic linear chains. The helical symmetry of the nanotube is taken into consideration by describing the nanotube structure using a helical-angular construction of the nanotube 11 and the in-teractions between the atoms are considered in terms of tight-binding parameters for and orbitals obtained from density-functional theory DFT as a function of the inter-atomic distances. 12,13 An important work discussing the ef-fect of strain in carbon nanotubes using a helical-symmetry-based first-principles calculation was published by Lawler et al. 14 Although, the presence of a natural torsion was not in-vestigated by these authors, it is expected that their method is appropriate for such a study and should be used to verify the simpler model calculations. Conceptually, SWNTs can be seen as a rolled up graphene sheet. In Fig. 1, the translational primitive cell of a 4,2 nanotube is shown. The chiral vector C h , that lies along the circumferential direction of the tube, defines the tube uniquely. This vector can be written as C h = na 1 + ma 2 in terms of the primitive vectors of the graphene honeycomb lattice a 1 and a 2 , also shown schematically in the figure, and the indexes n , m specify the carbon nanotube structure. This unit cell is bounded by the pure rotational symmetry vector C h / d, where d is the greatest common divisor of n and m d = gcdn , m, and by the pure translation vector T. Figure 1 shows the translation unit cell of a 4,2 SWNT and its structural parameters. 13 When a torsion is applied to the SWNT, the pure translational symmetry depicted by the translation vector T in Fig. 1 is broken. However, the screw translations, such as the one represented by the vector Z in Fig. 1, remain as symmetry operations of the nanotube. For this reason, it is possible to calculate the electronic properties of torsioned carbon nanotubes by using a helical-angular representation, 11 where the electronic states are labeled by a purely rotational quantum number , which is related to an angular momentum around the nanotube axis, and a helical quantum number h, which can be loosely related to a linear
[show abstract][hide abstract] ABSTRACT: We performed Raman spectroscopy experiments on undoped and boron-doped double walled carbon nanotubes (DWNTs) that exhibit the “coalescence inducing mode” as these DWNTs are heat treated to temperatures between 1200 °C and 2000 °C. The fact that boron doping promotes DWNT coalescence at lower temperatures allowed us to study in greater detail the behavior of first- and second-order Raman modes as a function of temperature with regard to the coalescence process. Furthermore, by using various excitation laser energies we probed DWNTs with different metallic (M) and semiconducting (S) inner and outer tubes. We find that regardless of their M and S configurations, the smaller diameter nanotubes disappear at a faster rate than their larger diameter counterparts as the heat treatment temperature is increased. We also observe that the frequency of the G band is mostly determined by the diameter of the semiconducting layer of those DWNTs that are in resonance with the laser excitation energy. Finally, we explain the contributions to the G′ band from the inner and outer layers of a DWNT. NSF/DMR Ministry of Education, Culture, Sports, Science and Technology of Japan Fondo Mixto de Puebla SALUD-CONACYT MIT-CONACYT Inter American Collaboration CONACYT Mexico
[show abstract][hide abstract] ABSTRACT: We used micro‐Raman spectroscopy and atomic force microscopy to study variations of the Raman spectrum as a function of the number of graphene layers. Samples were prepared by micromechanical cleaving of natural graphite on a ∼ 300‐nm SiO2 layer. The variations of Raman G band ( ∼ 1,580 cm−1), G∗ band ( ∼ 2,450 cm−1), and 2D band ( ∼ 2,700 cm−1) were observed as a function of the number of graphene layers. Raman 2D band is especially sensitive to the number of graphene layers. These features are related to the electronic band structure of graphene. Moreover, the areas of different number of graphene layers were clearly identified using spatially resolved micro‐Raman imaging spectroscopy. Polarized micro‐Raman spectroscopy on single‐layer graphene shows strong polarization dependences of double‐resonance Raman intensities. The Raman intensity of the double‐resonant 2D band is maximum when the excitation and detection polarizations are parallel and minimum when they are orthogonal, whereas that of the G band is isotropic. A calculation shows that this strong polarization dependence is a direct consequence of inhomogeneous optical absorption and emission mediated by electron‐phonon interactions involved in the second‐order Stokes‐Stokes Raman scattering process.
[show abstract][hide abstract] ABSTRACT: Raman spectroscopy was used to determine the dispersion of the longitudinal acoustic (LA) and in-plane transverse optic phonon branches near the Dirac K point of monolayer graphene from the analysis of the dispersion of two second-order Raman peaks involving the LA and TO phonons. We show that the velocities of the phonons involved in the double resonance Raman process are given by vLA=7.70×10-3vF and vTO=5.47×10-3vF , where vF is the Fermi velocity of the associated electrons. The experimental results for the phonon dispersion in monolayer graphene are compared with those for turbostratic graphite and also with different theoretical models.
Physical Review B 12/2007; 76(23). · 3.77 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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.
[show abstract][hide abstract] ABSTRACT: In this work, we performed a detailed study of the Raman spectra of double-wall carbon nanotube DWNT bucky paper samples. The effects of H 2 SO 4 doping on the electronic and vibrational properties of the DWNTs are analyzed and compared to the corresponding effects on single-wall carbon nanotubes SWNTs. Analysis of the radial breathing mode RBM Raman spectra indicates that the resonance condition for the outer wall nanotubes and the SWNTs are almost the same, indicating that the effect of the inner-outer wall interaction on the transition energies of the outer walls is weak compared to the width of the resonance window for the RBM peaks. The effect of H 2 SO 4 on the RBM frequencies of the outer wall of the DWNTs is stronger for larger diameter nanotubes. In the case of the inner walls, only the metallic nanotubes were affected by the acid treatment, while the RBM peaks for the inner semiconducting nanotubes remained almost unchanged in both frequency and intensity. The G + band was seen to upshift in frequency with H 2 SO 4 doping for both DWNTs and SWNTs. However, the effect of the acid treatment on the G − band frequency for DWNTs was opposite to that of SWNTs in the 2.05– 2.15 eV range, for which the acid treatment causes a G − upshift for SWNTs and a downshift for DWNTs. The G band line shape of the DWNTs is explained in terms of four contributions from different components which are in resonance with the laser excitation. Two of these peaks are more related to the inner wall nanotube while the other two are more related to the outer wall.
[show abstract][hide abstract] ABSTRACT: The electron-phonon coupling in two-dimensional graphite and metallic single-wall carbon nanotubes is analyzed. The highest-frequency phonon mode at the K point in two-dimensional graphite opens a dynamical band gap that induces a Kohn anomaly. Similar effects take place in metallic single-wall carbon nanotubes that undergo Peierls transitions driven by the highest-frequency phonon modes at the and K points. The dynami-cal band gap induces a nonlinear dependence of the phonon frequencies on the doping level and gives rise to strong anharmonic effects in two-dimensional graphite and metallic single-wall carbon nanotubes.
[show abstract][hide abstract] ABSTRACT: We have studied the exciton properties of single-wall carbon nanotubes by solving the Bethe-Salpeter equation within tight-binding models. The screening effect of the π electrons in carbon nanotubes is treated within the random phase and static screened approximations. The exciton wave functions along the tube axis and circumference are discussed as a function of (n,m). A 2n+m=const family behavior is found in the exciton wave function length, excitation energy, binding energy, and environmental shift. This family behavior is understood in terms of the trigonal warping effect around the K point of a graphene layer and curvature effects. The large family spread in the excitation energy of the Kataura plot is found to come from the single-particle energy.
[show abstract][hide abstract] ABSTRACT: Within the framework of the tight-binding model, we have developed exciton-photon and exciton-phonon matrix elements for single-wall carbon nanotubes. The formulas for first-order resonance and double-resonance Raman processes are discussed in detail. The lowest-energy excitonic state possesses an especially large exciton-photon matrix element compared to other excitonic states and continuum band states because of its localized wave function with no node. Unlike the free-particle picture, the photon matrix element in the exciton picture shows an inverse diameter dependence but no tube type or chirality dependences. As a result, the optical absorption intensity shows a strong diameter dependence but no tube type or chirality dependences. Moreover, the continuum band edge can be determined from the wave function or exciton-photon matrix element. For the radial breathing mode (RBM) and G-band modes, the phonon matrix elements in the exciton and free-particle pictures are almost the same. As a result, the intensity for the Kataura plots for the RBM or G-band modes by the exciton and free-particle pictures show similar family patterns. However, the excitonic effect has greatly increased the diameter dependence and magnitude of the intensities for the RBM and G band by enhancing the diameter dependence and magnitude of the photon matrix element. Therefore, excitons have to be considered in order to explain the strong diameter dependence of the Raman signal observed experimentally.
[show abstract][hide abstract] ABSTRACT: In this work, we present a detailed Raman spectroscopy study of graphitic foams probing the spatial and laser excitation energy dependences of the double resonance Raman peaks. We have observed a spatial dependence of the D to G band intensity ratio (ID∕IG) and of the relative contribution from the two-dimensional (2D) and three-dimensional (3D) graphite regions to the G′ band in the Raman spectra. The D band integrated intensity was found to decrease linearly with increasing laser energy (EL), in contrast with recent experiments on nanographite, which showed an EL−4 dependence for the ID∕IG ratio. The calculation of the skewness of the G′ band was found to be a good qualitative measure of the relative density of 2D and 3D graphite in a given region of the sample. The direct comparison between the spatial distribution of defects, given by the ID∕IG ratio, and the presence of the 2D graphite phase, given by the skewness of the G′ band, suggests a correlation between the presence of defects and the high density of 2D graphite.
Physical Review B 01/2007; 76(3). · 3.77 Impact Factor
[show abstract][hide abstract] ABSTRACT: Although the Raman effect was discovered nearly 80 years ago, it is only recently that the special characteristics of Raman scattering for one-dimensional systems have been seriously considered. This review focuses on the special interest of the Raman effect for one-dimensional systems that is of particular relevance to carbon nanostructures. Two examples of Raman scattering in one-dimensional systems are given. The first illustrates the use of Raman spectroscopy to reveal the remarkable structure and properties of carbon nanotubes arising from their one-dimensionality. Some of the recent advances in using Raman spectroscopy to study doping and intercalation to modify nanotube properties are reviewed, in the context of a one-dimensional system. The second example is the Raman spectra of a linear chain of carbon atoms and the special properties of this interesting system. New approaches toward applying Raman spectroscopy to carbon nanostructures are also emphasized.
Physica E Low-dimensional Systems and Nanostructures 01/2007; 37:81-87. · 1.52 Impact Factor
[show abstract][hide abstract] ABSTRACT: We discuss here how the trigonal warping effect of the electronic structure is relevant to optical processes in graphite and carbon nanotubes. The electron-photon, electron-phonon, and elastic scattering matrix elements have a common factor of the coefficients of Bloch wave funtions of the A and B atoms in the graphite unit cell. Because of the three fold symmetry around the Fermi energy point (the K or K′ point), the matrix elements show a trigonal anisotropy which can be observed in both resonance Raman and photoluminescence spectroscopy. This anisotropy is essential for understanding the chirality dependence of the Raman intensity and the optical response of single wall carbon nanotubes.
[show abstract][hide abstract] ABSTRACT: The photoluminescence (PL) intensity of a single-wall carbon nanotube (SWNT) is calculated for each (n, m) by multiplying the photon-absorption, relaxation and photon-emission matrix elements. The intensity depends on chirality and “type I vs type II” for smaller diameter semiconducting SWNTs (less than 1 nm). By comparing the calculated results with the experimental PL intensity of SWNTs prepared by chemical vapor deposition at different temperatures, we find that the abundance of (n, m) nanotubes with smaller diameters should exhibit a strong chirality dependence, which may be related to the stability of their caps.
[show abstract][hide abstract] ABSTRACT: The Raman intensity of the disorder-induced D-band in graphitic materials is cal-culated as a function of the in-plane size of the graphite nanoparticles (L a) and as a function of the excitation laser energy. Matrix elements associated with the dou-ble resonance Raman processes, i.e., electron-photon, electron-phonon and electron-defect process are calculated based on the tight binding method. The electron-defect interaction is calculated by considering the elastic scattering at the armchair edge of graphite, adopting a nanographite flake whose width is L a . We compare the cal-culated results with the experimental results obtained from the spectra for different laser lines and L a .
Chemical Physics Letters - CHEM PHYS LETT. 01/2006; 427(1).
[show abstract][hide abstract] ABSTRACT: Using a confocal micro-Raman system, spectra showing the splitting of optical transitions due to trigonal warping effect are presented for metallic single-wall carbon nanotubes SWNT's. Our results indicate that the intensity variations between different optical transitions can be attributed primarily to the differences in the magnitude of the electron-phonon coupling matrix elements. Our approach will allow the study of the magni-tude of electron-phonon matrix elements as well as quantum interference effects between different transitions in metallic SWNT's.
[show abstract][hide abstract] ABSTRACT: In this Letter, we report the effects of strain on the electronic properties of single-wall carbon nanotubes. When we normalize the electronic transition energies to the corresponding values obtained for unstrained tubes, we obtain that, regardless of the tube diameter, all the data collapse onto universal curves following an n - m = constant family pattern. In the case of metallic tubes, quantum interference effects on the Raman cross section are predicted for strained tubes when the energies of the lower and the upper components have nearly the same values. Experimental evidence for the strain-induced Raman cross section changes is observed in single nanotube spectroscopy.