The electronic bandgaps measured in fluorescence spectroscopy on individual single wall carbon nanotubes isolated within micelles show signficant deviations from the predictions of one electron band theory. We resolve this problem by developing a theory of the electron hole interaction in the photoexcited states. The one dimensional character and tubular structure introduce a novel relaxation pathway for carriers photoexcited above the fundamental band edge. Analytic expression for the energies and lineshapes of higher subband excitons are derived, and a comparison with experiment is used to extract the value of the screened electron hole interaction.
@article{arxiv.cond-mat/0303528,
title = {The Ratio Problem in Single Carbon Nanotube Fluorescence Spectroscopy},
author = {C. L. Kane and E. J. Mele},
journal= {arXiv preprint arXiv:cond-mat/0303528},
year = {2009}
}