Nonlinear photoluminescence excitation spectroscopy of carbon nanotubes: exploring the upper density limit of one-dimensional excitons

We have observed that photoemission from single-walled carbon nanotubes saturates in intensity as the excitation intensity increases. Each emission peak arising from specific-chirality tubes exhibited a saturation value independent of the excitation wavelength, suggesting an upper limit on the exciton density for each nanotube species. We developed a model based on diffusion-limited exciton-exciton annihilation, which allowed us to estimate exciton densities in the saturation regime. The estimated densities were found to be still substantially smaller than the expected Mott density.