Exciton-exciton annihilation and relaxation pathways in semiconducting carbon nanotubes

We present a thorough analysis of one- and two-color transient absorption measurements performed on single-and double-walled semiconducting carbon nanotubes. By combining the currently existing models describing exciton-exciton annihilation-the coherent and the diffusion-limited ones-we are able to simultaneously reproduce excitation kinetics following both E-11 and E-22 pump conditions. Our simulations revealed the fundamental photophysical behavior of one-dimensional coherent excitons and non-trivial excitation relaxation pathways. In particular, we found that after non-linear annihilation a doubly-excited exciton relaxes directly to its E-11 state bypassing the intermediate E-22 manifold, so that after excitation resonant with the E-11 transition, the E-22 state remains unpopulated. A quantitative explanation for the observed much faster excitation kinetics probed at E-22 manifold, comparing to those probed at the E-11 band, is also provided.