Dynamics of a three-component delocalized nonlinear vibrational mode in graphene

The dynamics of a three-component nonlinear delocalized vibrational mode in graphene is studied with molecular dynamics. This mode, being a superposition of a root and two one-component modes, is an exact and symmetrically determined solution of nonlinear equations of motion of carbon atoms. The dependences of a frequency, energy per atom, and average stresses over a period that appeared in graphene are calculated as a function of amplitude of a root mode. We showed that the vibrations become periodic with certain amplitudes of three component modes, and the vibrations of one-component modes are close to periodic one and have a frequency twice the frequency of a root mode, which is noticeably higher than the upper boundary of a spectrum of low-amplitude vibrations of a graphene lattice. The data obtained expand our understanding of nonlinear vibrations of graphene lattice.