Quantized Bimolecular Auger Recombination of Excitons in Single-Walled Carbon Nanotubes

Auger-like exciton-exciton annihilation in isolated single-walled carbon nanotubes (SWNTs) has been studied by femtosecond transient absorption spectroscopy. We observe a quantization of the Auger recombination process and extract dynamics for 2 and 3 electron-hole pair excited states. We further demonstrate that Auger recombination in SWNTs is a two-particle process involving strongly bound excitons and not a three-particle Auger process involving unbound electrons and holes. We thus provide explicit experimental evidence for one-dimensional discrete excitons in SWNTs.

Figure 1

(a) Population decay probed at 1245 nm for pump fluences: 2.0 (circles), 20 (diamonds), and $200\times {10}^{13}\mathrm{\text{photons}}/{\mathrm{cm}}^2$ (triangles). Lines are fits based on the quantized Auger recombination model of Ref. 29. Inset: Cross correlation of the pump and probe pulse (dashed line) and transient absorption signal (circles) probed at 1323 nm. The solid line is a convolution between a Gaussian excitation pulse and the function $(1-e^{-t/{\tau }_r})\times e^{-t/{\tau }_i}$ with ${\tau }_r=110\pm 20\mathrm{fs}$ and ${\tau }_i=1.2\mathrm{ps}$. (b) Population decay dynamics ($\mathrm{\text{probe}}=1245\mathrm{nm}$) with increasing pump intensity, where all curves have been normalized. The pump fluences from bottom to top are $2,4,8,20\times {10}^{13}\mathrm{\text{photons}}/{\mathrm{cm}}^2$ (lowest group); $5,8,10,20\times {10}^{14}\mathrm{\text{photons}}/{\mathrm{cm}}^2$ (middle group); and 3.4 and $5\times {10}^{15}\mathrm{\text{photons}}/{\mathrm{cm}}^2$ (top group). The increase of the signal at 700 fs arises because of a slight structure in the pump pulse temporal profile, which has a negligible contribution to all electron-hole pair lifetimes. Inset: $\Delta T/T$ ($\mathrm{\text{probe}}=1245\mathrm{nm}$) as a function of pump fluence (circles). The solid line is a linear fit to $y=1.6\times {10}^{-16}x$. (c) Raw transient absorption population decay curves (circles) with quantitative fits (lines) based on the quantized Auger recombination model of Ref. 29. Inset: Schematic diagram illustrating quantized steps of Auger recombination in SWNTs.

Figure 2

The 1 $e\mathrm{\text{−}}h$ pair state dynamics (inset) and 2 (solid circles) and 3 (open circles) $e\mathrm{\text{−}}h$ pair dynamics extracted from transient absorption data probed at 1323 nm and fitted to a single exponential decay (solid lines).

Figure 3

$[⟨N_0⟩/⟨N_t⟩]-1$ (open symbols) and $[⟨N_0⟩/⟨N_t⟩{]}^2-1$ (solid symbols) vs time for a probe wavelength of 1170 nm (circles), 1245 nm (diamonds), and 1323 nm (triangles).