High-Energy Phonon Branches of an Individual Metallic Carbon Nanotube

We present excitation-energy dependent Raman measurements between 2.05 and 2.41 eV on the same individual carbon nanotube. We find a change in the Raman frequencies of both the $D$ mode ($63{\mathrm{c}\mathrm{m}}^{-1}/\mathrm{e}\mathrm{V}$) and the high-energy modes. The observed frequencies of the modes at $\approx 1600{\mathrm{c}\mathrm{m}}^{-1}$ as a function of laser-energy map the phonon dispersion relation of a metallic tube near the $\Gamma$ point of the Brillouin zone. Our results prove the entire first-order Raman spectrum in single-wall carbon nanotubes to originate from double-resonant scattering. Moreover, we confirm experimentally the phonon softening in metallic tubes by a Peierls-like mechanism.

Figure 1

Atomic-force microscopy image of a $6\times 6\mu {\mathrm{m}}^2$ area of the sample. Several isolated tubes or very thin bundles are dispersed on the substrate. The white circle indicates the investigated tube close to the four vertical electrodes.

Figure 2

Raman spectra of the same tube recorded at different laser energies (given next to the spectra). The spectra are scaled to about the same amplitudes and offset vertically. The vertical solid lines indicate the frequencies of the $D$ mode and the HEM peaks in the spectrum taken at 2.05 eV.

Figure 3

Left: High-energy mode frequencies as a function of excitation energy. The solid and dashed lines are a guide to the eye to sketch the proposed resemblance of the phonon dispersion relation of a chiral and an achiral metallic tube, respectively. Right: Calculated high-energy phonon frequencies of the (8,8) tube as a function of laser energy (top axis) and of the double-resonant phonon wave vector (bottom axis); dashed line as on the left. The relation between laser energy and phonon wave vector is not linear.

Figure 4

Experimental $D$-mode frequency as a function of excitation energy (dots) and calculated values for the (8,8) tube (triangles). The solid (dashed) line is a linear fit to the experimental data (theory). Inset: Relative Raman intensity (peak area normalized to laser power, integration time, and spectrometer sensitivity) of the HEM as a function of laser energy.