Chirality dependence of many body effects of single wall carbon nanotubes

The higher lying exciton energies (E33S and E44S) of single wall carbon nanotubes (SWNTs) are calculated by solving the Bethe–Salpeter equation within an extended tight binding method. For E11S and E22S transitions, the chirality dependence of the exciton binding energy for each (n,m)(n,m) SWNT is almost cancelled by that of the self energy. Thus the origin of the family pattern for E11S and E22S can be understood by the chirality dependence of the single particle energies. However, for E33S and E44S transitions, since the self energy becomes larger than the exciton binding energy, the chirality dependence of many body effects becomes important to analyze the transition energies.