Nonlinear vibrational modes in graphene: group-theoretical results

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.