Theoretical study of the doping effect on the phonon dispersion of metallic carbon nanotubes

The phonon dispersion of all metallic carbon nanotubes in the diameter range from 0.8 to 3.0 nm was calculated using a perturbative approach within a density-functional-based symmetry-adapted non-orthogonal tight-binding model. The obtained dispersion curves, corrected for non-adiabatic effects, exhibit Kohn anomalies at the Brillouin zone centre and at two mirror points inside the zone. These anomalies are efficiently removed upon charge doping for Fermi energy shift larger than 0.3 eV, which is illustrated in the case of nanotube (12,0). The obtained results for the G band frequencies of all the nanotubes in the studied diameter range confirm previous theoretical results.