Chirality dependence of many body effects of single wall carbon nanotubes

The higher lying exciton energies (E₃₃^S and E₄₄^S) of single wall carbon nanotubes (SWNTs) are calculated by solving the Bethe-Salpeter equation within an extended tight binding method. For E₁₁^S and E₂₂^S transitions, the chirality dependence of the exciton binding energy for each (n, m) SWNT is almost cancelled by that of the self energy. Thus the origin of the family pattern for E₁₁^S and E₂₂^S can be understood by the chirality dependence of the single particle energies. However, for E₃₃^S and E₄₄^S 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.