Valentin Popov's

NANOTUBE AND GRAPHENE PROJECT


Nanotube structure

Relaxed structure

Electronic structure

Zone-folding method

NTB model intro

NTB application

Optical absorption

Dielectric function

Effective mass

Electron-photon

Resonance chart

Phonon dispersion

Graphene

Zone-folding method

FC model

NTB model

FC, NTB application

Γ-phonons

Phonon symmetry

Eigenvectors

Frequencies

Elastic properties

Elastic moduli

Bulk modulus

Heat capacity

T-dependence

Low-T heat capacity

Raman scattering

RBM intensity

Electron-phonon

NTB results

Approximations

Tabulated data

Graphical data

JAVA Applet

G-band intensity

NTB results

Approximations

Graphics & tables


PROJECT

SUPPORT

NATO ASI

NATO CRG

NATO SRF

NATO CLG

 

UA RAFO

 

OSTC

 

 

MEIF

MERG

 

http://www.pa.msu.edu/~tomanek/NTlogo.jpg

The NanotubeSite

HOME

STRUCTURE

ELECTRONS

PHONONS

RAMAN

PUBLICATIONS

 

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

 

 

 

 

up

 

ELECTRONIC STRUCTURE

The electronic structure of any nanotube can be derived from that of graphene by use of the zone-folding 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 symmetry-adapted non-orthogonal tight-binding model (NTB model). Read more

 

up

 

OPTICAL ABSORPTION

The optical absorption is characterized by the dielectric function. It depends on the effective mass of the transition and the electron-photon 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   

 

up

 

PHONON DISPERSION

The phonon dispersion of any nanotube can be derived from that of graphene by use of the zone-folding method. This method does not yield the phonon eigenvectors. The direct calculation of the phonon dispersion of the relaxed nanotube is rather time-consuming if possible at all. However, it can be obtained for any observable nanotube in symmetry-adapted models. Examples: force-constant models (FC models) and a non-orthogonal tight-binding model (NTB model). Read more

 

 

up

 

Γ-PHONONS

For each nanotube there are four acoustic and numerous optical Γ-phonons, 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 radial-breathing mode (RBM) and up to six tangential modes (G-modes), which give rise to intense Raman lines. Read more

 

 

 

up

 

LINEAR ELASTIC PROPERTIES

The small-stress 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 small-stress 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

 

 

up

 

HEAT CAPACITY

The low-temperature phonon heat capacity of nanotubes can simply be derived from the quantum-mechanical formula. At very-low 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 quasi-three-dimensional one. Read more  

 

 

 

up 

 

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

 

 

 

up

 

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 electron-phonon 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

 

 

up

 

G-BAND INTENSITY

The Raman data on the G-modes is not widely used for characterization purposes, the reasons for this being different for the different G-modes. However, the Raman G-band can be useful for distinguishing between metallic and semiconducting nanotubes, and for determination of the doping level. The RRP of the most intense A1 G-modes 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

 

up

 

 

RECENT PUBLICATIONS

 

DOUBLE-RESONANT RAMAN SPECTRA OF SILICENE

 

Two-phonon Raman spectra

2D Materials 3 (2016) 025014 arXiv

 

DOUBLE-RESONANT RAMAN SPECTRA OF FEW-LAYER GRAPHENE

 

Two-phonon Raman spectra

Carbon 91 (2015) 436 arXiv

 

Low-frequency phonon dispersion

Phys. Rev. B 90 (2014) 245429. arXiv

 

DOUBLE-RESONANT RAMAN SPECTRA OF GRAPHENE

 

2D, 2D', D+D'', Raman bands

Eur. Phys. J. B 85 (2012) 418 arXiv

Read more

 

Strain Dependence of the Raman bands

Carbon 54 (2013) 86

Phys. Rev. B 87 (2013) 155425 arXiv

Read more

 

DOPING OF GRAPHENE AND NANOTUBES

 

Kohn anomalies

Dynamic effects

Doping effects

 

Phys. Rev. B 82 (2010) 045406.

Nano Research 3 (2010) 822.

 

POINT DEFECTS IN GRAPHENE AND NANOTUBES

 

Mono-vacancies

Di-vacancies

Stone-Wales defects

Raman spectra

 

Carbon 47 (2009) 2448.

 

 

 

Back to my home page

Valentin Popov

28.04.2016