Publications (77)188.29 Total impact
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ABSTRACT: The D band Raman intensity is calculated for armchair edged graphene nanoribbons using an extended tightbinding 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 longrange 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 wellknown 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 06/2011; 83(24). · 3.66 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 intertubule interactions. More systematic studies will be required to better understand the effects of inhomogeneous broadening and thermalexcitation on the detailed position and lineshape of the low frequency phonon features in carbon nanotubes.MRS Proceedings. 12/2010; 1284.  [Show abstract] [Hide abstract]
ABSTRACT: In this work we investigate the presence of a torsional instability in singlewall 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 tightbinding 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 neararmchair 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 applicability of nanotubes for electromechanical actuators, the torsional properties of multiwall and singlewall carbon nanotubes SWNTs have been widely investigated both experimentally and theoretically. 4–10 However, for the interpretation of these works, these reports assume that in their natural state, carbon nanotubes are free from such geometrical 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 parameters 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 representation 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 application 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 finitelength nanotubes or in supercells. However, these studies were able to obtain important information about the mechanical properties of nanotubes. One interesting result was reported by Liang et al., 9 which showed that the relationship between the axialstraininduced 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 singlewall carbon nanotube is dependent 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 natural torsion in chiral singlewall carbon nanotubes by using a symmetryadapted tightbinding calculation. The presence of this natural torsion is explained in terms of a torsional instability 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 helicalangular construction of the nanotube 11 and the interactions between the atoms are considered in terms of tightbinding parameters for and orbitals obtained from densityfunctional theory DFT as a function of the interatomic distances. 12,13 An important work discussing the effect of strain in carbon nanotubes using a helicalsymmetrybased firstprinciples calculation was published by Lawler et al. 14 Although, the presence of a natural torsion was not investigated 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 helicalangular 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 linearPhysical review. B, Condensed matter 04/2010; 81(16):165430. · 3.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We performed Raman spectroscopy experiments on undoped and borondoped 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 secondorder 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 SALUDCONACYT MITCONACYT Inter American Collaboration CONACYT MexicoPhysical review. B, Condensed matter 07/2009; · 3.66 Impact Factor  [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.AIP Conference Proceedings. 04/2009; 1119(1):232232.  Physical Review B 01/2009; · 3.66 Impact Factor
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ABSTRACT: Raman spectroscopy was used to determine the dispersion of the longitudinal acoustic (LA) and inplane transverse optic phonon branches near the Dirac K point of monolayer graphene from the analysis of the dispersion of two secondorder 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=7.70×103vF and vTO=5.47×103vF , 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). · 3.66 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 (MSWNTs) as a function of Fermi level (epsilonF) position, by tuning a polymer electrolyte gate. Our study focuses on the data from MSWNTs 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 MSWNTs 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 Asymmetry LO phonon mode frequency due to a Kohn anomaly in MSWNTs.Physical Review Letters 11/2007; 99(14):145506. · 7.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this work, we performed a detailed study of the Raman spectra of doublewall 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 singlewall 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 innerouter 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.Physical review. B, Condensed matter 07/2007; 76(045425):045425. · 3.66 Impact Factor  [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 twodimensional (2D) and threedimensional (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 07/2007; 76(3). · 3.66 Impact Factor 
Article: Electronphonon coupling mechanism in twodimensional graphite and singlewall carbon nanotubes
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ABSTRACT: The electronphonon coupling in twodimensional graphite and metallic singlewall carbon nanotubes is analyzed. The highestfrequency phonon mode at the K point in twodimensional graphite opens a dynamical band gap that induces a Kohn anomaly. Similar effects take place in metallic singlewall carbon nanotubes that undergo Peierls transitions driven by the highestfrequency phonon modes at the and K points. The dynamical band gap induces a nonlinear dependence of the phonon frequencies on the doping level and gives rise to strong anharmonic effects in twodimensional graphite and metallic singlewall carbon nanotubes.Physical review. B, Condensed matter 04/2007; 75(15):155420. · 3.66 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 onedimensional systems have been seriously considered. This review focuses on the special interest of the Raman effect for onedimensional systems that is of particular relevance to carbon nanostructures. Two examples of Raman scattering in onedimensional systems are given. The first illustrates the use of Raman spectroscopy to reveal the remarkable structure and properties of carbon nanotubes arising from their onedimensionality. 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 onedimensional 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 Lowdimensional Systems and Nanostructures 03/2007; 37:8187. · 1.86 Impact Factor 
Article: Chirality dependence of exciton effects in singlewall carbon nanotubes: Tightbinding model
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ABSTRACT: We have studied the exciton properties of singlewall carbon nanotubes by solving the BetheSalpeter equation within tightbinding 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 singleparticle energy.Physical review. B, Condensed matter 01/2007; 75(3). · 3.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Within the framework of the tightbinding model, we have developed excitonphoton and excitonphonon matrix elements for singlewall carbon nanotubes. The formulas for firstorder resonance and doubleresonance Raman processes are discussed in detail. The lowestenergy excitonic state possesses an especially large excitonphoton matrix element compared to other excitonic states and continuum band states because of its localized wave function with no node. Unlike the freeparticle 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 excitonphoton matrix element. For the radial breathing mode (RBM) and Gband modes, the phonon matrix elements in the exciton and freeparticle pictures are almost the same. As a result, the intensity for the Kataura plots for the RBM or Gband modes by the exciton and freeparticle 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.Physical review. B, Condensed matter 01/2007; 75(3). · 3.66 Impact Factor  Physical Review B 01/2007; · 3.66 Impact Factor
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ABSTRACT: We discuss here how the trigonal warping effect of the electronic structure is relevant to optical processes in graphite and carbon nanotubes. The electronphoton, electronphonon, 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.Molecular Crystals and Liquid Crystals 10/2006; 455(1):287294. · 0.49 Impact Factor 
Article: Dband Raman intensity of graphitic materials as a function of laser energy and crystallite size
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ABSTRACT: The Raman intensity of the disorderinduced Dband in graphitic materials is calculated as a function of the inplane size of the graphite nanoparticles (L a) and as a function of the excitation laser energy. Matrix elements associated with the double resonance Raman processes, i.e., electronphoton, electronphonon and electrondefect process are calculated based on the tight binding method. The electrondefect 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 calculated results with the experimental results obtained from the spectra for different laser lines and L a .Chemical Physics Letters 08/2006; 427(1). · 1.99 Impact Factor 
Article: Raman characterization of electronic transition energies of metallic singlewall carbon nanotubes
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ABSTRACT: Using a confocal microRaman system, spectra showing the splitting of optical transitions due to trigonal warping effect are presented for metallic singlewall 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 electronphonon coupling matrix elements. Our approach will allow the study of the magnitude of electronphonon matrix elements as well as quantum interference effects between different transitions in metallic SWNT's.Physical review. B, Condensed matter 08/2006; 74(7). · 3.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The photoluminescence (PL) intensity of a singlewall carbon nanotube (SWNT) is calculated for each (n, m) by multiplying the photonabsorption, relaxation and photonemission 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.Carbon. 01/2006;  [Show abstract] [Hide abstract]
ABSTRACT: We have developed the electronphonon matrix element in singlewall carbon nanotubes by using the extended tightbinding model based on density functional theory. We calculate this matrix element to study the electronphonon coupling for the radial breathing mode (RBM) and the Gband A symmetry modes of singlewall carbon nanotubes. Three welldefined family patterns are found in the RBM, longitudinal optical (LO) mode and transverse optical (TO) mode. We find that among the RBM, LO, and TO modes, the LO mode has the largest electronphonon interaction. To study the electronphonon coupling in the transport properties of metallic nanotubes, we calculate the relaxation time and mean free path in armchair tubes. We find that the LO mode, A1′ mode, and one of the E1′ modes give rise to the dominant contributions to the electron inelastic backscattering by phonons. Especially, the offsite deformation potential gives zero matrix elements for E1′ modes while the onsite deformation potential gives rise to nonzero matrix elements for the two E1′ modes, indicating that the onsite deformation potential plays an important role in explaining the experimentally observed Raman mode around 2450 cm−1 in carbon.Physical review. B, Condensed matter 12/2005; 72(23). · 3.66 Impact Factor
Publication Stats
2k  Citations  
188.29  Total Impact Points  
Top Journals
Institutions

2007–2011

University of California, Berkeley
 Department of Physics
Berkeley, CA, United States


2010

Lawrence Berkeley National Laboratory
 Materials Sciences Division
Berkeley, CA, United States


2002–2009

Massachusetts Institute of Technology
 • Department of Electrical Engineering and Computer Science
 • Department of Chemistry
Cambridge, MA, United States


2005

Universidade Federal do Ceará
 Departamento de Física
Fortaleza, Estado do Ceara, Brazil


2003–2004

Federal University of Minas Gerais
 Departamento de Física
Belo Horizonte, Estado de Minas Gerais, Brazil
