Ultrafast Exciton Dephasing in Semiconducting Single-Walled Carbon Nanotubes

Femtosecond two-pulse degenerate four-wave mixing spectroscopy was applied to study the exciton dephasing in a broad range of excitation intensities and lattice temperatures. We find that both exciton-exciton and exciton-phonon scattering have profound effects on the dephasing process. The dominant phonon mode involved in the dephasing is identified as the out-of-plane, transverse optical mode with a frequency of $847{\mathrm{cm}}^{-1}$. The extracted homogeneous linewidths at all measured temperatures are in excellent agreement with the results of a single-tube photoluminescence experiment.

Figure 1

Linear absorption spectrum of the SWNT/PVP film (light line). The peaks at 571 and 990 nm correspond to the second and the first excitonic transitions of the dominant tube species in the sample, the (6, 5) tube. The black line is the laser pulse spectrum. Both spectra are normalized at the maxima.

Figure 2

(a) Schematic of the geometry of four-wave mixing. Here $t_{12}$ is considered positive (negative) when pulse 1 (2) precedes pulse 2 (1). (b) FWM signals measured at 100 K for five different excitation intensities. (c) FWM signals measured at 77, 130, 200, and 292 K under the lowest excitation intensity used for this experiment, which was $\sim 1.70\mu \mathrm{J}/{\mathrm{cm}}^2$. The dashed line is the autocorrelation function of the two laser pulses. All the data have been normalized at the signal maxima.

Figure 3

Dependence of the dephasing rates and the corresponding homogeneous linewidths on excitation intensity at different lattice temperatures. (a) 77, 100, and 130 K, (b) 160, 200, 250, and 292 K. The solid lines in (a) are the linear fits to the data obtained at 77, 100, and 130 K. The dashed lines in (b) are drawn to guide the eye. The corresponding exciton densities estimated from the absorption cross section, mean tube length, laser beam size at the focus, and the excitation intensities are depicted by the scales on the top of the plots.

Figure 4

The dephasing rates in the zero-intensity limit versus temperature. The solid line is a least squares fit. The corresponding homogeneous linewidths are depicted by the scales on the right side. See text for details. The crosses at 77, 100, and 130 K show the $1/T_2(0)$ values obtained through linear extrapolation of the data in Fig. 3a.