Electron-phonon coupling mechanism, Kohn anomalies and Peierls instabilities in two-dimensional graphite and single-wall carbon nanotubes*

The electron-phonon coupling in two-dimensional graphite and metallic single-wall carbon nanotubes (SWNTs) is analyzed. The $G'$-band phonon mode opens a dynamical band gap that induces a Kohn anomaly in two-dimensional graphite, while truly metallic armchair SWNTs undergo Peierls transitions driven by the $G$- and $G'$-band phonon modes. The dynamical band gap induces a non-linear dependence of the phonon frequencies on the doping level and gives rise to strong anharmonic effects.