Exciton–exciton annihilation and relaxation pathways in semiconducting carbon nanotubes

Abstract

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 E₁₁ and E₂₂ 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 E₁₁ state bypassing the intermediate E₂₂ manifold, so that after excitation 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 the E₁₁ band, is also provided.