Intensity-Dependent Exciton Dynamics of (6,5) Single-Walled Carbon Nanotubes: Momentum Selection Rules, Diffusion, and Nonlinear Interactions

The exciton dynamics for an ensemble of individual, suspended (6,5), single-walled carbon nanotubes revealed by single color E(22) resonant pump-probe spectroscopy for a wide range of pump fluences are reported. The optically excited initial exciton population ranges from approximately 5 to 120 excitons per similar to 725 nm nanotube. At the higher fluences of this range, the pump probe signals are no longer linearly dependent on the pump Intensity. A single, predictive model is described that fits all data for two decades of pump fluences and three decades of delay times. The model introduces population loss from the optically active zero momentum E(22) state to the rest of the E(22) subband, which Is dark due to momentum selection rules. In the single exciton limit, the E(11) dynamics are well described by a stretched exponential, which is a direct consequence of diffusion quenching from an ensemble of nanotubes of different lengths. The observed change in population relaxation dynamics as a function of increasing pump intensity is attributed to exciton exciton Auger de-excitation in the E(11) subband and, to a lesser extent, in the E(22) subband. From the fit to the model, an average defect density 1/rho = 150 nm and diffusion constants D(11) = 4 cm(2)/s and D(22) = 0.2 cm(2)/s are determined.