Exciton-exciton annihilation in single-walled carbon nanotubes

The femtosecond fluorescence and transient absorption kinetics recorded on selected semiconducting single-walled carbon nanotubes exhibit pronounced excitation-intensity-dependent decays as the result of exciton-exciton annihilation. A satisfactory description of the decays obtained at various excitation intensities, however, requires a time-independent annihilation rate that is valid only for extended systems with dimensionality greater than 2 in conjunction with diffusive migration of excitons. We resolved this apparent contradiction by developing a stochastic model, in which we assumed that the exciton states in semiconducting nanotubes are coherent, and the multiexciton manifolds are resonantly coupled with other excited states, which decay by subsequent linear relaxation due to electron-phonon coupling. The formalism derived from this model enables a qualitative description of the experimental results for the (9,5), (8,3), and (6,5) semiconducting single-walled carbon nanotubes.