Phonons in graphene with point defects

Abstract

The phonon density of states (DOS) of graphene with different types of point defects(carbon isotopes, substitution atoms, vacancies) is considered. Using a solvable modelwhich is based on the harmonic approximation and the assumption that the elasticforces act only between nearest neighboring ions we calculate corrections to thegraphene DOS dependent on the type and concentration of defects. In particular thecorrection due to isotopic dimers is determined. It is shown that a relatively smallconcentration of defects may lead to significant and specific changes in the DOS,especially at low frequencies, near the Van Hove points and in the vicinity of the Kpoints of the Brillouin zone. In some cases defects generate one or several narrowgaps near the critical points of the phonon DOS as well as resonance states inthe Brillouin zone regular points. All types of defects are characterized by theappearance of one or more additional Van Hove peaks near the (Dirac) K points andtheir singular contribution may be comparable with the effect of electron–phononinteraction. Besides, for low frequencies and near the critical points the relativechange in density of states may be many times higher than the concentration ofdefects.