Exciton energy calculations for single wall carbon nanotubes

Using the Bethe-Salpeter equation, we have calculated the exciton energies of (i) bright exciton states; (ii) 2g exciton energies; and (iii) the energy difference between dark and bright exciton states for single wall carbon nanotubes (SWNTs) as a function of diameter. By adjusting the dielectric constant, we can reproduce the observed exciton energies in the resonance Raman spectra and two-photon absorption spectra for SWNTs. The environmental effect on the transition energies can be explained by a diameter-dependent dielectric constant. However, the energy difference between the dark and bright exciton states cannot be reproduced simply by changing the dielectric constant consistently. Thus we need to consider the evaluation of the Coulomb interaction, especially with regard to the surrounding materials.