Rasmussen, Morten Grud and Ricaud, Benjamin and Savoie, Baptiste (2015) On the optical properties of carbon nanotubes. Part I. A general formula for the dynamical optical conductivity. Journal of Mathematical Physics, 57 (2). 021901. ISSN 00222488

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Abstract
This paper is the first one of a series of two articles in which we revisit the optical properties of singlewalled carbon nanotubes (SWNT). Produced by rolling up a graphene sheet, SWNT owe their intriguing properties to their cylindrical quasionedimensional (quasi1D) structure (the ratio length/radius is experimentally of order of 10^3 ). 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 pairinteraction potential considered is the 3D Coulomb potential restricted to the cylinder. To reflect the quasi1D structure, we introduce a 1D effective manybody Hamiltonian which is the startingpoint of our analysis. To investigate the optical properties, we consider a perturbation by a uniform timedependent 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 lowtemperature 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 manybody Hamiltonian, and allows us to account for the sharp peaks observed in the optical absorption spectrum of SWNT.
Item Type:  Article 

Uncontrolled Keywords:  Carbon nanotube, SWNT, optical conductivity, optical absorption spectrum, linear response theory, Kubo’s method. 
Divisions:  School of Theoretical Physics > Preprints 
Date Deposited:  05 Oct 2017 19:30 
Last Modified:  26 Jul 2018 10:49 
URI:  http://dair.dias.ie/id/eprint/333 
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