Kohn Anomaly in Raman Spectroscopy of Single Wall Carbon Nanotubes

TL;DR

This paper reviews the theoretical understanding of phonon softening, including the Kohn anomaly, in metallic single wall carbon nanotubes, focusing on the effects of curvature, Fermi energy, and chirality on Raman-active phonon modes.

Contribution

It introduces a unified effective-mass model with a deformation-induced gauge field to analyze curvature effects and electron-phonon interactions in nanotubes.

Findings

Curvature induces a mini-energy gap affecting phonon softening.

Fermi energy and chirality influence the phonon softening phenomena.

The effective-mass model provides a comprehensive framework for these effects.

Abstract

Phonon softening phenomena of the $\Gamma$ point optical modes including the longitudinal optical mode, transverse optical mode and radial breathing mode in "metallic" single wall carbon nanotubes are reviewed from a theoretical point of view. The effect of the curvature-induced mini-energy gap on the phonon softening which depends on the Fermi energy and chirality of the nanotube is the main subject of this article. We adopt an effective-mass model with a deformation-induced gauge field which provides us with a unified way to discuss the curvature effect and the electron-phonon interaction.