Resonant Raman Scattering of the Smallest Single-Walled Carbon Nanotubes

We report optical properties of the smallest single-walled carbon nanotubes (SWNTs) with a diameter of only 3 Å. These ultrasmall SWNTs are fabricated in the elliptical nanochannels of an AlPO-11 (AEL) single crystal. Polarized and resonant Raman scattering unambiguously revealed that these 0.3 nm SWNTs are of (2,2) armchair symmetry. Interestingly, the (2,2) armchair tube has two metastable ground states corresponding to two slightly different lattice constants in the axial direction: one state is metallic and the other is semiconducting.

Figure 1

(a) Scanning electron microscope image of AEL single crystals. (b) The crystal structure. The dark spheres represent oxygen atoms and the light spheres denote Al or P atoms. (c) The 10-ring channel, viewed along (001) direction. An armchair (2,2) carbon nanotube is also sketched inside.

Figure 2

Raman spectrum of a SWNT@AEL single crystal. The vertical bars at the bottom are frequencies of the Raman-active modes for the (2,2) armchair SWNT calculated using a density functional approximation. The Raman spectra measured using different excitation laser wavelengths are plotted in the inset.

Figure 3

Polarized Raman spectra in the $G^{+}$ band region collected under (a) perpendicular excitation and (b) parallel excitation in three polarization configurations. Polar diagrams in the lower panel show the Raman intensities of the $A_{1g}$ mode (solid circles) as a function of the angle $\theta$ between the polarization of the incident light and the nanotube axis under the $VV$ polarization configuration measured at an excitation laser beam perpendicular [$P(a)$] to and along [$P(b)$] the tube direction.

Figure 4

(a) Raman spectra in the low-frequency region excited using different laser lines. (b) The integrated resonant Raman intensity plotted as a function of excitation photon energy. (c) The calculated total energy of the (2,2) nanotube plotted as a function of $c$-axis lattice constant. (d) The calculated dielectric functions of the (2,2) carbon nanotube corresponding to the two ground state structures of $c=2.485\AA$ (solid line) and $c=2.580\AA$ (dotted line), respectively.