One Dimensional Exciton Diffusion on Semiconducting Nanotubes using Time Resolved Photoabsorption Spectroscopy

We extend our recently reported analysis of the population relaxation of optically excited states on semiconducting carbon nanotubes to study the spectral shifts of their photoabsorption spectra. Highly excited tubes show a long time $1/\sqrt t $ decay of their photobleaching spectra which is well described by a one dimensional diffusion limited two body population relaxation. We find that the absorption spectra also show time-dependent spectral shifts with respect to the ground state absorption spectra. The spectral shifts are of order 10 nm and history dependent: two tubes prepared from different initial excitation densities but evolving to the same instantaneous excitation density show different lineshapes and spectral shifts. These features are analyzed by a model for the distribution of exciton separations produced in a diffusing population. The model provides an excellent parameter free description of the lineshape, and gives an estimate of the experimental exciton diffusion constant.