Excitons in single-wall carbon nanotubes

Excitonic states in single-wall carbon nanotubes have been studied within the tight-binding approximation. An analytical expression for the dielectric function of the nanotube has been obtained in the random phase approximation. It was demonstrated that calculations with the static dielectric function yield an overestimated exciton binding energy exceeding the nanotube energy gap. Self-consistent calculation of the exciton binding energy with the frequency-dependent dielectric function has been performed. The binding energy to energy gap ratio has been shown to have no dependence on the nanotube radius and to be a universal constant similar to 0.87 for given resonance integral gamma(o) = 2.7 eV.