Symmetry constraints on phonon dispersion in graphene

TL;DR

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

Contribution

It introduces analytical formulas for phonon modes in graphene considering up to third nearest neighbors, enhancing understanding of lattice dynamics.

Findings

Analytical expressions for out-of-plane phonon modes with nonzero sound velocity.

Fitted force constants to experimental frequencies and elastic constants.

Detailed phonon dispersion relations for graphene's in-plane and out-of-plane modes.

Abstract

Taking into account the constraints imposed by the lattice symmetry, we calculate the phonon dispersion for graphene with interactions between the first, second, and third nearest neighbors in the framework of the Born--von Karman model. Analytical expressions obtained for the dispersion of the out-of-plane (bending) modes give the nonzero sound velocity. The dispersion of four in-plane modes is determined by coupled equations. Values of the force constants are found in fitting with frequencies at critical points and with elastic constants measured on graphite.