Elastic Exciton-Exciton Scattering in Photoexcited Carbon Nanotubes

We report on original nonlinear spectral hole-burning experiments in single wall carbon nanotubes that bring evidence of pure dephasing induced by exciton-exciton scattering. We show that the collision-induced broadening in carbon nanotubes is controlled by exciton-exciton scattering as for Wannier excitons in inorganic semiconductors, while the population relaxation is driven by exciton-exciton annihilation as for Frenkel excitons in organic materials. We demonstrate that this singular behavior originates from the intrinsic one-dimensionality of excitons in carbon nanotubes, which display unique hybrid features of organic and inorganic systems.

Figure 1

Exciton energy dispersion and schematic representation of the Auger recombination process of exciton-exciton annihilation (EEA, in blue), and the purely dephasing mechanism of elastic exciton-exciton scattering (EES, in red). The dashed lines delimitate the exciton paths in $k$ space for EEA and EES.

Figure 2

Left axis: Differential transmission $\Delta T/T$ of the probe laser at 10 K with a pump laser of $4\mathrm{kW}{\mathrm{cm}}^{-2}$ at 0.8 eV, as a function of the probe laser energy. The red solid curve is the sum of the differential transmissions $\Delta T/T$ calculated for $\Delta \Gamma =0$ (blue dotted line) and $\Delta f=0$ (green dashed line). Right axis: Optical density (dashed line) spectrum obtained by linear absorption spectroscopy of the carbon nanotubes gelatin sample. Inset: (right axis) Optical density displayed on a large spectral range. The red vertical arrow indicates the pump laser energy of 0.8 eV used for hole-burning measurements in semiconducting carbon nanotubes. Photoluminescence intensity (left axis) under nonresonant excitation at 2.33 eV.

Figure 3

(a) Relative variations of the homogeneous linewidth $\Delta \Gamma /\Gamma$ (full circles) and oscillator strength $-\Delta f/f$ (open squares) at 10 K. Data (symbols) and theoretical fits (solid lines) are plotted as a function of the incident power of the pump laser. The fitting parameter is the exciton Bohr radius $a_B=5\mathrm{nm}$, and the shaded areas correspond to the tolerance of $\pm 2\mathrm{nm}$ in its estimation. (b) Homogeneous linewidth variations $\Delta \Gamma$ as a function of pump power. Theoretical fits: EEA only (blue line), $\mathrm{EEA}+\mathrm{EES}$ (red line).