Exciton-exciton annihilation and relaxation pathways in semiconducting carbon nanotubes

We present a thorough analysis of two-color transient absorption measurements performed on single- and double-walled semiconducting carbon nanotubes (CNTs). By combining currently existing models describing exciton-exciton annihilation – the coherent and the diffusion-limited ones – we are able to simultaneously reproduce excitation kinetics following both E11 and E22 pump conditions at a time range from several fs up to tens ps. We found that after non-linear annihilation a doubly-excited excitons relaxes directly to its E11 state bypassing the intermediate E22 manifold, so that after excitation, being resonant with the E11 transition, the E22 state remains unpopulated. A quantitative explanation for the observed much faster excitation kinetics probed at E22 manifold, comparing to those probed at E11 band, is also provided.