Two-photon photoluminescence and exciton binding energies in single-walled carbon nanotubes

We compare experimental one- and two-photon luminescence excitation spectra of single-walled carbon nanotubes at room temperature to ab initio calculations. The experimental spectra reveal a Rydberg-like series of excitonic states. The energy splitting between these states is a clear fingerprint of excitonic correlations in carbon nanotubes. From those spectra, we derive exciton binding energies of 0.3-0.4 eV for nanotubes with diameters between 6.8 angstrom and 9.0 angstrom. These energies are in quantitative agreement with our nanotubes with diameters between 6.8 angstrom and 9.0 angstrom. These energies are in quantitative agreement with our theoretical calculations, which predict the symmetries of the relevant excitonic wave functions and indicate that a low-lying optically dark excitonic state may be responsible for the low luminescence quantum yields in nanotubes.