Electron-phonon coupling mechanism in two-dimensional graphite and single-wall carbon nanotubes

The electron-phonon coupling in two-dimensional graphite and metallic single-wall carbon nanotubes is analyzed. The highest-frequency phonon mode at the $K$ point in two-dimensional graphite opens a dynamical band gap that induces a Kohn anomaly. Similar effects take place in metallic single-wall carbon nanotubes that undergo Peierls transitions driven by the highest-frequency phonon modes at the $\Gamma$ and $K$ points. The dynamical band gap induces a nonlinear dependence of the phonon frequencies on the doping level and gives rise to strong anharmonic effects in two-dimensional graphite and metallic single-wall carbon nanotubes.