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Modélisation et étude des propriétés optiques des nanotubes de carbone

Abstract : The optical absorption spectrum of carbon nanotubes is analysed, using a rigourous mathematical approach. A quantum model describing the carbon nanotube is suggested and investigated with the help of perturbation theory. The smallness of the tube radius allows to reduce the study to a one dimensional problem. Then, the linear response theory gives an expression for the absorption spectrum depending on the eigenstates of the one-dimensional Hamiltonian associated with the tube. Several physical arguments as well as an intensive use of perturbation theory allow to reduce the study of the many body Hamiltonian to the study of the exciton Hamiltonian, which describes a system made of two particles with opposite charges. Quasi-analytical expressions for the eigenstates of this system, depending on the radius of the tube, are obtained perturbatively. Peaks of absorption of light with energy in the gap between the valence and conduction bands of the semiconductor nanotube are related to the existence of excitons and the localisation of the peaks is given with respect to the radius of the nanotube by an approximated expression, with a controled error term.
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Contributor : Benjamin Ricaud <>
Submitted on : Tuesday, October 30, 2007 - 3:50:53 PM
Last modification on : Thursday, March 15, 2018 - 4:56:04 PM
Long-term archiving on: : Friday, November 25, 2016 - 6:42:17 PM


  • HAL Id : tel-00183627, version 2


Benjamin Ricaud. Modélisation et étude des propriétés optiques des nanotubes de carbone. Physique mathématique [math-ph]. Université du Sud Toulon Var, 2007. Français. ⟨tel-00183627v2⟩



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