Steplike dispersion of the intermediate-frequency Raman modes in semiconducting and metallic carbon nanotubes

Resonance Raman spectra of semiconducting and metallic single-wall carbon nanotube bundles have been investigated in the spectral range between 600 and $1100{\mathrm{cm}}^{-1}$, which is associated with intermediate frequency modes. A large range of nanotube diameters corresponding to HiPco and electric-arc samples $(0.7–1.8\mathrm{nm})$, and laser excitation energies between 1.62 and $2.71\mathrm{eV}$ have been used in the measurements. A rich set of peaks is observed, some of them independent of the excitation laser energy and some exhibiting a steplike dispersive behavior. The nondispersive peaks are assigned. The model proposed by Fantini et al. [Phys. Rev. Lett. 93, 087401 (2004)] to explain the steplike dispersive behavior of the intermediate frequency modes is then extended to different SWNT diameters and different $E_{ii}$ transitions, including semiconducting and metallic SWNTs.

Figure 1

Raman spectrum of SWNT bundles (electric-arc) obtained with excitation laser energy $E_{\text{laser}}=2.41\mathrm{eV}$. The well-studied features, namely the radial breathing mode (RBM), the disorder-induced (D) band, and the graphitelike (G) band features are assigned. The intensity for the intermediate frequency mode (IFM) region is multiplied by 30 to clearly show the richness of the low intensity IFM spectral region that is the focus of this work.

Figure 2

Raman spectra of the IFMs for the electric-arc sample obtained by changing the laser energy between 1.63 and $2.71\mathrm{eV}$. The arrows in the figure represent the six well-resolved and step-like dispersive IFM peaks previously observed (Ref. 11) below the first-order peak at ${\omega }_{\mathrm{oTO}}\sim 860{\mathrm{cm}}^{-1}$. The shaded areas mark the nondispersive features.

Figure 3

Raman spectra of the IFMs for the HiPco sample obtained by changing the laser energy between 1.62 and $2.71\mathrm{eV}$. The arrows in the figure represent the four well-resolved and steplike dispersive IFM peaks below the first-order peak at ${\omega }_{\mathrm{oTO}}\sim 845{\mathrm{cm}}^{-1}$. The shaded areas mark the nondispersive features.

Figure 4

$E_{\text{laser}}$ vs ${\omega }_{\mathrm{IFM}}$ for all the steplike dispersive IFM peaks observed in the two samples. The bars are the resonance energy range over which each IFM peak is observed. Black bars with diagonal lines and gray bars with horizontal lines come from arc samples and HiPco, respectively. The dashed and solid lines are the fit of the experimental data for samples 1 and 2, respectively.

Figure 5

Schematic picture for the allowed electronic transitions mediated by phonons for a (a) semiconducting $S1$ $(2n+m\mathrm{mod}3=1)$ SWNT (20,0) and (b) metallic SWNT (15,0).

Figure 6

Plot of the electronic transition energies $\left(E_{ii}\right)$ vs nanotube diameter $\left(d_t\right)$ obtained from the corrected extended tight-binding model, showing the diameter distribution for HiPco (solid rectangle) and arc electric (dashed rectangle) nanotube samples. The bars in the energy scale correspond to the energy range over which each IFM peak is in resonance, and their widths reflect the error in the $d_t$ calculation coming from the fitting data fitting.