Higher energy optical transitions in semiconducting carbon nanotubes

We have studied the high energy optical transitions of semiconducting single-walled carbon nanotubes using the nonorthogonal tight-binding model, which takes into account the exciton effect. It is found from our calculations that the exciton's binding energies for the high energy E(33) and E(44) transitions are large enough, indicating clearly they are also excitonic in nature. More importantly, the logarithmic Kane-Mele correction, successful for the low energy E(11) and E(22) transitions, is now found to fail for describing the many-body effects in the higher energy transitions, which is consistent with the experimental result of Araujo et al (2007 Phys. Rev. Lett. 98 067401). Finally, it is interesting to find the possibility of a crossover effect between the E(33) and E(44) energies for certain mod 1 chiralities and the family behavior of the many-body corrections in the E(33) and E(44) transitions, both of which are well supported by the recent experiment of Haroz et al (2008 Phys. Rev. B 77 125405).