Symmetry based analysis of the Kohn anomaly and electron-phonon interaction in graphene and carbon nanotubes

Abstract

Symmetry based analysis of the electron-phonon coupling in graphene and carbon nanotubes is performed and Kohn anomalies, their Brillouin-zone positions together with the complete set of good quantum numbers are predicted. Interestingly, graphene dynamical representation is found to contain only a small portion of quite a large set of inequivalent irreducible representations of the relevant full symmetry group. Besides, vanishing of the electron-phonon interaction for majority of the normal displacements is also shown to be a consequence of the symmetry. The results are further numerically confirmed within full and tight-binding density-functional calculations and force constants model and enhanced coupling to the Fermi level electrons of the Dirac point ${A}_{1g}$ mode with respect to the $\ensuremath{\Gamma}$ point ${E}_{2g}$ mode is confirmed. Finally, energy dispersion of the kink phonon spectrum is analytically evaluated and compared to the classical phonon spectrum.