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Title: On the optical properties of carbon nanotubes. Part I. A general formula for the dynamical optical conductivity

This paper is the first one in a series of two articles in which we revisit the optical properties of single-walled carbon nanotubes (SWNTs). Produced by rolling up a graphene sheet, SWNTs owe their intriguing properties to their cylindrical quasi-one-dimensional (quasi-1D) structure (the ratio length/radius is experimentally of order of 10{sup 3}). We model SWNT by circular cylinders of small diameters on the surface of which the conduction electron gas is confined by the electric field generated by the fixed carbon ions. The pair-interaction potential considered is the 3D Coulomb potential restricted to the cylinder. To reflect the quasi-1D structure, we introduce a 1D effective many-body Hamiltonian which is the starting-point of our analysis. To investigate the optical properties, we consider a perturbation by a uniform time-dependent electric field modeling an incident light beam along the longitudinal direction. By using Kubo’s method, we derive within the linear response theory an asymptotic expansion in the low-temperature regime for the dynamical optical conductivity at fixed density of particles. The leading term only involves the eigenvalues and associated eigenfunctions of the (unperturbed) 1D effective many-body Hamiltonian and allows us to account for the sharp peaks observed in the optical absorption spectrum of SWNT.
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg (Denmark)
  2. Laboratoire de Traitement des Signaux 2, École Polytechnique Fédérale de Lausanne, Lausanne, Vaud (Switzerland)
  3. Dublin Institute for Advanced Studies, School of Theoretical Physics, 10 Burlington Road, Dublin 04 (Ireland)
Publication Date:
OSTI Identifier:
22479625
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 2; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ABSORPTION SPECTRA; ASYMPTOTIC SOLUTIONS; CARBON NANOTUBES; COULOMB FIELD; EIGENFUNCTIONS; EIGENVALUES; GRAPHENE; HAMILTONIANS; OPTICAL PROPERTIES; PAIRING INTERACTIONS