Analytic Study of the Susceptibility of Carbon Nanotubes by Including the Overlap between Third Nearest Neighbors

Including third-nearest neighbors interactions, tight-binding description of electronic dispersion reproduces the first-principle calculations for graphene as well as carbon nanotubes [S. Reich, et all, Phys. Rev. B 66, 035412(2012)]. Using a simple tight-binding method up to the third nearest neighbor interactions and considering the orbital overlap between wave functions, the energy dispersion, the electric dipole matrix elements and the linear electric susceptibility as a function of optical frequency of some single wall carbon nanotubes for light polarized parallel to the nanotube axis are investigated. The linear electric susceptibility obtained up to the third nearest neighbors including orbital overlap is compared with those obtained for the first nearest neighbors. The calculations show a red shift in linear electric susceptibility including third neighbors in comparison with those including only first nearest neighbors.