Structural dependence of excitonic optical transitions and band-gap energies in carbon nanotubes

The optical transitions of semiconducting carbon nanotubes have been ascribed to excitons. Here we use two-photon excitation spectroscopy to measure exciton binding energies, as well as band-gap energies, in a range of individual species of semiconducting SWNTs. Exciton binding energies are large and vary inversely with nanotube diameter, as predicted by theory. Band-gap energies are significantly blue-shifted from values predicted by tight-binding calculations.