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

TL;DR

This paper predicts how the radial breathing mode frequency in metallic carbon nanotubes varies with Fermi energy, showing chirality-dependent shifts linked to electron-phonon interactions and curvature effects.

Contribution

It introduces a theoretical model explaining chirality-dependent phonon frequency shifts in metallic nanotubes based on electron-phonon coupling and curvature-induced energy gaps.

Findings

Armchair nanotubes show no frequency shift.

Zigzag nanotubes exhibit phonon softening.

Radial breathing mode intensity exceeds that of the G band.

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.