Non-adiabatic phonon dispersion of metallic single-walled carbon nanotubes

Non-adiabatic effects can considerably modify the phonon dispersion of low-dimensional metallic systems. Here, these effects are studied for the case of metallic single-walled carbon nanotubes using a perturbative approach within a density-functional-based non-orthogonal tight-binding model. The adiabatic phonon dispersion was found to have logarithmic Kohn anomalies at the Brillouin zone center and at two mirror points inside the zone. The obtained dynamic corrections to the adiabatic phonon dispersion essentially modify and shift the Kohn anomalies as exemplified in the case of nanotube (8, 5). Large corrections have the longitudinal optical phonon, which gives rise to the so-called G- band in the Raman spectra, and the carbon hexagon breathing phonon. The results obtained for the G- band for all nanotubes in the diameter range from 0.8 to 3.0 nm can be used for assignment of the high-frequency features in the Raman spectra of nanotube samples.