Exciton binding energies in carbon nanotubes from two-photon photoluminescence

Excitonic effects in the linear and nonlinear optical properties of single-walled carbon nanotubes are manifested by photoluminescence excitation experiments and ab initio calculations. One- and two-photon spectra showed a series of exciton states; their energy splitting is the fingerprint of excitonic interactions in carbon nanotubes. By ab initio calculations we determine the energies, wave functions, and symmetries of the excitonic states. Combining experiment and theory we find binding energies of $0.3\char21{}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for nanotubes with diameters between 6.8 and $9.0\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$.