
Valentin Popov's
NANOTUBE AND GRAPHENE PROJECT


PROJECT SUPPORT
NATO ASI NATO CRG NATO SRF NATO CLG
UA RAFO
OSTC
MEIF MERG


MAIN TOPICS OF THE PROJECT
NANOTUBE
STRUCTURE
The carbon nanotubes have a screw symmetry characterized generally by two screw operations. The screw symmetry of the nanotubes allows one to use only four structural parameters in the structural relaxation. Read more …
ELECTRONIC STRUCTURE
The electronic structure of any nanotube can be derived from that of graphene by use of the zonefolding method. This method suffers the severe drawback of not being able to predict the electronic wave functions. The calculations of the electronic structure for the relaxed nanotube can efficiently be performed for any observable nanotube only if the screw symmetry is accounted for. An example: a symmetryadapted nonorthogonal tightbinding model (NTB model). Read more …
OPTICAL
ABSORPTION
The optical absorption is characterized by the dielectric function. It depends on the effective mass of the transition and the electronphoton matrix element. For nanotubes, it has sharp spikes at the energies of the optical transitions. Since Raman scattering of light in nanotubes is essentially resonant, the knowledge of the optical transitions can be used in combination with Raman spectra for characterization of the samples. The first realistic estimation of the optical transitions was done within the NTB model. Read more …
PHONON DISPERSION
The phonon dispersion of any nanotube can be derived from that of graphene by use of the zonefolding method. This method does not yield the phonon eigenvectors. The direct calculation of the phonon dispersion of the relaxed nanotube is rather timeconsuming if possible at all. However, it can be obtained for any observable nanotube in symmetryadapted models. Examples: forceconstant models (FC models) and a nonorthogonal tightbinding model (NTB model). Read more …
ΓPHONONS
For each nanotube there are four acoustic and numerous optical Γphonons, which can be classified by their symmetry. The optical phonons can further be put into four groups according to their atomic displacements. For Raman spectroscopy most important are the radialbreathing mode (RBM) and up to six tangential modes (Gmodes), which give rise to intense Raman lines. Read more …
LINEAR ELASTIC PROPERTIES
The smallstress elastic properties of nanotube systems are described by the elastic moduli – Young's modulus and shear modulus. Nanotubes are often observed in large bundles. Their smallstress elastic properties are characterized by the elastic constants and bulk modulus. Due to the different dominant force along and perpendicular to the bundle axis, the elastic properties of the bundles are highly anisotropic. Moreover, these properties depend strongly on the nanotube radii. Read more …
HEAT
CAPACITY
The lowtemperature phonon heat capacity of nanotubes can simply be derived from the quantummechanical formula. At verylow temperatures (T < ~1 K) the specific heat is determined by the transverse acoustic phonons. At higher temperatures (~1 < T < ~10 K) the heat capacity is due to longitudinal and twist acoustic phonons. The bundling of nanotubes smears this behavior to a quasithreedimensional one. Read more …
RAMAN SCATTERING OF LIGHT
In Raman scattering experiments on nanotubes, the Raman intensity depends strongly on the laser excitation, given by the resonance Raman profile (RRP). In particular, the Raman signal is enhanced whenever the laser line is in the resonant window, determined by the optical transitions. This feature is used in combination with Raman data for nanotube characterization. Read more …
RBM INTENSITY
The Raman data on the RBM is most often used for nanotube characterization because the RBM frequency is inversely proportional to the nanotube radius. The RRP of the RBM requires the knowledge of the electronphonon matrix element and can be done exactly or approximately (see comparison of both approaches). The exact NTB results for the Raman intensity amplitude can conveniently be used in a tabular, graphical, or JAVA Applet form. Read more …
GBAND INTENSITY
The Raman data on the Gmodes is not widely used for characterization purposes, the reasons for this being different for the different Gmodes. However, the Raman Gband can be useful for distinguishing between metallic and semiconducting nanotubes, and for determination of the doping level. The RRP of the most intense A1 Gmodes can be calculated exactly or approximately. The exact NTB results for the Raman intensity amplitude ca be used in tabular and graphical form. Read more …

RECENT
PUBLICATIONS
DOUBLERESONANT
RAMAN SPECTRA OF SILICENE
Twophonon Raman
spectra 2D Materials 3 (2016) 025014 arXiv DOUBLERESONANT RAMAN SPECTRA OF
FEWLAYER GRAPHENE
Twophonon Raman spectra
Lowfrequency phonon dispersion Phys. Rev. B 90 (2014) 245429. arXiv DOUBLERESONANT RAMAN SPECTRA OF
GRAPHENE
2D, 2D', D+D'', … Raman bands Eur. Phys. J. B 85 (2012) 418 arXiv
Strain Dependence of the Raman bands Phys. Rev. B 87 (2013) 155425 arXiv
DOPING
OF GRAPHENE AND NANOTUBES
Kohn anomalies Dynamic effects Doping effects
Phys. Rev. B 82 (2010) 045406.
POINT DEFECTS IN GRAPHENE AND
NANOTUBES
Monovacancies Divacancies StoneWales defects Raman spectra

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Valentin Popov
28.04.2016