Chirality dependent frequency shift of radial breathing mode in metallic carbon nanotubes

Abstract

A phonon frequency shift of the radial breathing mode for metallic single wall carbon nanotubes is predicted as a function of Fermi energy. Armchair nanotubes do not show any frequency shift while zigzag nanotubes exhibit phonon softening, but this softening is not associated with the broadening. This chirality dependence originates from a curvature-induced energy gap and a special electron-phonon coupling mechanism for radial breathing modes. Because of the particle-hole symmetry, only the off-site deformation potential contributes to the frequency shift. On the other hand, the on-site potential contributes to the Raman intensity, and the radial breathing mode intensity is stronger than that of the $G$ band. The relationship between the chirality dependence of the frequency shift of the radial breathing mode and the $\Gamma$ point optical phonon frequency shift is discussed.

arXiv comment12 pages, 7 figures

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• Kohn Anomaly in Raman Spectroscopy of Single Wall Carbon Nanotubes
• Origin of electronic Raman scattering and the Fano resonance in metallic carbon nanotubes
• Chiral Gauge Theory for Graphene Edge
• Theory of intraband plasmons in doped carbon nanotubes: rolled surface-plasmons of graphene
• Coherent radial breathing like phonons in graphene nanoribbons
• Valley-antisymmetric potential in graphene under dynamical deformation
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