Band-Gap Modulation and Kohn Anomalies in Two-Dimensional Graphite and Single-Wall Carbon Nanotubes

ABSTRACTThe electron-phonon coupling in two-dimensional graphite (graphene sheet) and metallic single-wall carbon nanotubes (SWNTs) is analyzed. In the graphene sheet the G-band phonon mode induces oscillations of the Fermi points, while the G′-band phonon mode opens a dynamical (oscillating with the phonon frequency) band gap, and accordingly, both phonon modes exhibit Kohn anomalies. Similarly, truly metallic armchair SWNTs undergo Peierls transitions driven by the G−- and G′-band phonon modes both of which open a dynamical band gap. In addition, the dynamical band gap induces a non-linear dependence of the phonon frequencies on the doping level and gives rise to strong anharmonic effects in the graphene sheet and metallic SWNTs.