Nonlinear vibrational modes in graphene: group-theoretical results

TL;DR

This paper uses group-theoretical methods to identify specific nonlinear vibrational modes in stretched graphene, revealing a limited set of symmetry-determined normal modes as exact solutions.

Contribution

The study applies group-theoretical techniques to find all possible nonlinear vibrational modes in graphene, including new classifications of one to four-dimensional bushes of nonlinear normal modes.

Findings

Identified 4 one-dimensional NNMs in graphene.

Discovered 14 two-dimensional, 1 three-dimensional, and 6 four-dimensional vibrational bushes.

All modes are exact solutions to the dynamical equations of graphene.

Abstract

In-plane nonlinear delocalized vibrations in uniformly stretched single-layer graphene (space group P6mm) are considered with the aid of the group-theoretical methods. These methods were developed by authors earlier in the framework of the theory of the bushes of nonlinear normal modes (NNMs). We have found that only 4 symmetry-determined NNMs (one-dimensional bushes), as well as 14 two-dimensional, 1 three-dimensional and 6 four-dimensional vibrational bushes are possible in graphene. They are exact solutions to the dynamical equations of this two-dimensional crystal. Prospects of further research are discussed.