Fluence-dependent singlet exciton dynamics in length-sorted chirality-enriched single-walled carbon nanotubes

We utilize individualized, length-sorted (6,5)-chirality enriched single-walled carbon nanotubes (SWNTs) having dimensions of 200 and 800 nm, femtosecond transient absorption spectroscopy, and variable excitation fluences that modulate the exciton density per nanotube unit length, to interrogate nanotube exciton/biexciton dynamics. For pump fluences below 30 μJ/cm ², transient absorption (TA) spectra of (6,5) SWNTs reveal the instantaneous emergence of the exciton to biexciton transition (E ₁₁→E_11,BX) at 1100 nm; in contrast, under excitation fluences exceeding 100 μJ/cm², this TA signal manifests a rise time (τ_rise ∼ 250 fs), indicating that E₁₁ state repopulation is required to produce this signal. Femtosecond transient absorption spectroscopic data acquired over the 900-1400 nm spectral region of the near-infrared (NIR) region for (6,5) SWNTs, as a function of nanotube length and exciton density, reveal that over time delays that exceed 200 fs exciton-exciton interactions do not occur over spatial domains larger than 200 nm. Furthermore, the excitation fluence dependence of the E₁₁→ E_11,BX transient absorption signal demonstrates that relaxation of the E₁₁ biexciton state (E_11,BX) gives rise to a substantial E₁₁ state population, as increasing delay times result in a concomitant increase of E₁₁→E_11,BX transition oscillator strength. Numerical simulations based on a three-state model are consistent with a mechanism whereby biexcitons are generated at high excitation fluences via sequential SWNT ground- and E₁₁-state excitation that occurs within the 980 nm excitation pulse duration. These studies that investigate fluence-dependent TA spectral evolution show that SWNT ground→E₁₁ and E₁₁→E_11,BX excitations are coresonant and provide evidence that E_11,BX→E₁₁ relaxation constitutes a significant decay channel for the SWNT biexciton state over delay times that exceed 200 fs, a finding that runs counter to assumptions made in previous analyses of SWNT biexciton dynamical data where exciton-exciton annihilation has been assumed to play a dominant role.