Anharmonic Phonon Lifetimes in Carbon Nanotubes: Evidence for a One-Dimensional Phonon Decay Bottleneck

High-resolution Raman spectroscopy is applied to suspended single-walled carbon nanotubes (SWNTs) to elucidate the puzzling differences in the lifetime of the radial breathing mode (RBM) obtained from different experimental techniques. Whereas recent tunneling experiments suggest a room temperature RBM lifetime as long as 10 ns , previous Raman experiments yield lifetimes shorter than 2 ps. The lifetimes obtained in this study are longer than 5 ps—a significant step in the direction of the tunneling results. We argue that the remaining discrepancy is due to the existence of phonon decay bottlenecks caused by the one-dimensional nature of nanotubes. Numerical simulations of the RBM decay show that it is possible to reconcile the short lifetimes measured spectroscopically with the long lifetimes obtained in tunneling experiments.

Figure 1

Raman spectra around the RBM frequency for two suspended SWNTs collected for different incident laser powers. From the shape of the tangential band near $1590{\mathrm{cm}}^{-1}$, panels (a) and (b) are assigned to metallic and semiconducting SWNTs, respectively.

Figure 2

Deconvoluted $2\Gamma$ (Lorentzian FWHM) values for several suspended SWNTs plotted versus the RBM frequency. The circled data points represent metallic SWNTs while the rest are semiconducting SWNTs.

Figure 3

Normalized linewidth versus incident total laser power $P$ (The normalized linewidth is defined as the Lorentzian FWHM at $P$ divided by the FWHM at $P=1\mathrm{mW}$). The lines show predictions from Eq. (2) for different values of $L$.

Figure 4

(a) Solid line: Raman phonon population decay under conditions that create a decay bottleneck due to the reduced phase space for secondary phonons ($p\sim 2$). This is the most realistic assumption for carbon nanotubes, Dotted line: Raman phonon population decay under conditions in which the decay bottleneck is negligible ($p\gg 1$), Dashed-dotted line: Raman phonon population decay when the secondary phonons are also created by the external perturbation, as could be the case in a tunneling experiment; (b) predicted Raman spectrum corresponding to the solid line in panel (a). The sharp central spike corresponds to the long lifetime tail in panel (a); (c) Solid line: Modeled observed Raman spectrum obtained from convoluting the spectrum in panel (b) with a Gaussian function that represents a typical instrumental resolution. Dotted line: Fit of the solid line using a Voigt profile, as typically done to extract the Lorentzian linewidth from the observed experimental line shape. The extracted Lorentzian linewidth represents the broad tail in panel (b), whereas information from the central spike is lost in the convolution process. Thus it is not possible to detect the long lifetime component in a Raman experiment.