Curvature induced optical phonon frequency shift in metallic carbon nanotubes

TL;DR

This paper theoretically investigates how curvature affects the quantum corrections to optical phonon frequencies in metallic carbon nanotubes, revealing curvature-dependent shifts and decoupling phenomena near the Gamma point.

Contribution

It introduces a theoretical analysis of curvature-induced quantum frequency shifts and mode decoupling in metallic carbon nanotubes, highlighting electron-phonon interactions and symmetry effects.

Findings

Frequency shift depends on curvature and Fermi energy.

TO mode decouples from electrons near Gamma point.

No phonon mixing between LO and TO modes due to symmetry.

Abstract

The quantum corrections to the frequencies of the $\Gamma$ point longitudinal optical (LO) and transverse optical (TO) phonon modes in carbon nanotubes are investigated theoretically. The frequency shift and broadening of the TO phonon mode strongly depend on the curvature effect due to a special electron-phonon coupling in carbon nanotubes, which is shown by the Fermi energy dependence of the frequency shift for different nanotube chiralities. It is also shown that the TO mode near the $\Gamma$ point decouples from electrons due to local gauge symmetry and that a phonon mixing between LO and TO modes is absent due to time-reversal symmetry. Some comparison between theory and experiment is presented.