Discontinuity in the family pattern of single-wall carbon nanotubes

The higher lying bright exciton energies (E-11(M),E-33(S),E-44(S),E-22(M),E-55(S),E-66(S),E-33(M)) of single-wall carbon nanotubes are calculated by solving the Bethe-Salpeter equation within an extended tight binding method. For smaller diameter nanotubes, some higher E-ii excitonic states are missing. In particular, some E-ii's on the one-dimensional Brillouin zone (cutting line) are no longer relevant to the formation of excitons and are skipped in listing the order of the E-ii values. Thus the family patterns show some discontinuities in k space and this effect should be observable in Raman G(') band spectroscopy. The higher exciton energies E-33(S) and E-44(S) have a large chirality dependence due to many body effects, since the self-energy becomes larger than the binding energy. Thus the chirality dependence of the higher E-ii comes not only from a single particle energy but also from many-body effects.