Double resonance features in the Raman spectrum of carbon nanotubes

A weak feature is observed in the Raman spectra of single-wall carbon nanotube bundles at a frequency between 1410 and $1430{\mathrm{cm}}^{-1}$. The band shifts slightly toward lower frequencies as the excitation energy increases from 2.17 to $2.71\mathrm{eV}$. An inverse correlation is found between the frequency of the band and that of the average radial-breathing mode, indicating a dependence on the nanotube diameter. The frequency can be extrapolated quadratically to $1487{\mathrm{cm}}^{-1}$ for infinite diameter. Two different hypotheses are considered, ascribing the band to modes around either $K$ or $M$ points of the graphite dispersion relations. The appearance of a band close to $1480{\mathrm{cm}}^{-1}$ in defective graphite and its dependence with the laser energy, as well as the strong sensitivity of high-frequency $K$-point modes to structural or impurity defects, support the interpretation of the mode as arising from for the upper phonon branch of graphite around the $K$ point activated by the double-resonance mechanism.

Figure 1

Raman spectra of SWNT bundles. The long spectrum corresponds to the raw soot material prior to purification and is measured at $E_{\mathrm{L}}=2.41\mathrm{eV}$. The inset shows the evolution of the $G$-band region with $E_{\mathrm{L}}$ from 2.17 to $2.71\mathrm{eV}$, as indicated on the right-hand side. The spectra have been normalized to the same $G$-band intensity. The sample used for the spectra of the inset had been heated at $300°\mathrm{C}$ for $1\mathrm{h}$.

Figure 2

(a) The frequency of feature $F$, ${\nu }_{\mathrm{F}}$, is plotted against the average frequency of the radial-breathing mode,${\nu }_{\mathrm{RBM}}$, indicating that a correlation exists between ${\nu }_{\mathrm{F}}$ and the NT diameter. The dashed line is the fitting of the data to a quadratic expression of the form ${\nu }_0+C^{\prime }{\nu }_{\mathrm{RBM}}^x$ with ${\nu }_0=1487.4{\mathrm{cm}}^{-1}$, $C^{\prime }=-\mathrm{0.0\hspace{0.17em}029\hspace{0.17em}331}{\mathrm{cm}}^{0.96}$, and $x=1.96$. (b) Correlation between ${\nu }_{\mathrm{F}}$ and the frequency of the lowest component of the $G$ band, $G^{-}$. The dashed line is only a guide for the eye. Data were taken at $2.41\mathrm{eV}$.