Phonons in graphene with point defects

TL;DR

This paper models how various point defects in graphene alter its phonon density of states, revealing significant and specific changes even at low defect concentrations, especially near critical phonon points.

Contribution

It introduces a solvable harmonic model to quantify defect-induced corrections to graphene's phonon DOS, including isotopic dimers and defect-generated gaps and resonance states.

Findings

Defects cause notable changes in phonon DOS at low frequencies and critical points.

Introduction of Van Hove peaks near K points due to defects.

Small defect concentrations can significantly alter phonon properties.

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 model which is based on the harmonic approximation and the assumption that the elastic forces act only between nearest neighboring ions we calculate corrections to graphene DOS dependent on type and concentration of defects. In particular the correction due to isotopic dimers is determined. It is shown that a relatively small concentration 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 K-points of the Brillouin zone. In some cases defects generate one or several narrow gaps near the critical points of the phonon DOS as well as resonance states in the Brillouin zone regular points. All types of defects are characterized by the appearance of one or more additional Van Hove peaks near the (Dirac) K points and their singular contribution may be comparable with the effect of electron-phonon interaction. Besides, for low frequencies and near the critical points the relative change in density of states may be many times higher than the concentration of defects.