Kohn Anomaly in Raman Spectroscopy of Single Wall Carbon Nanotubes

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.