Optical Properties of Small-Radius SWNTs within a Tight-Binding Model

Abstract

The optical properties of single-walled carbon nanotubes (SWNTs) are studied within a symmetry-adapted density-functional-theory-based non-orthogonal tight-binding model using 2s and 2p electrons of carbon. The use of symmetry-adapted model for the calculation of the electronic band structure and the optical properties allows reducing significantly the size of the matrix electronic eigenvalue problem. Consequently, it could be possible to do these calculations for all 48 SWNTs with radii between 2 Å and 5 Å. The obtained band structures for several nanotube types agree well with ab-initio results up to ∼ 3.5 eV above the Fermi energy. Similarly to the ab-initio calculations, the tight-binding model predicts deviations from the predictions of the band structure within the zone-folding method. It is demonstrated that, e.g., nanotube (5,0) is metallic while the zone-folding method predicts it as semiconducting. Secondly, the dielectric function for the same nanotube types is calculated within the random phase approximation for energies up to 7 eV. The peak positions of the imaginary part of the dielectric function for parallel light polarisation versus nanotube radius are illustrated on a chart.