Phonon dispersion in graphene

TL;DR

This paper calculates the phonon dispersion in graphene considering lattice symmetry and interactions up to second nearest neighbors, providing analytical expressions and fitting force constants to experimental data.

Contribution

It introduces analytical formulas for phonon modes in graphene based on symmetry and extends the Born-von Karman model with fitted force constants.

Findings

Analytical expressions for out-of-plane and in-plane phonon modes.

Force constants fitted to elastic and Raman data.

Enhanced understanding of phonon behavior in graphene.

Abstract

Taking into account the constraints imposed by the lattice symmetry, the phonon dispersion is calculated for graphene with interactions between the first and second nearest neighbors in the framework of the Born-von Karman model. Analytical expressions are obtained for the out-of-plane (bending) modes determined only by two force constants as well as for the in-plane modes with four force constants. Values of the force constants are found in fitting to elastic constants and Raman frequencies observed in graphite.