Delocalized Nonlinear Vibrational Modes in Graphene: Second Harmonic Generation and Negative Pressure

With the help of molecular dynamics simulations, delocalized nonlinear vibrational modes (DNVM) in graphene are analyzed. Such modes are dictated by the lattice symmetry, they are exact solutions to the atomic equations of motion, regardless the employed interatomic potential and for any mode amplitude (though for large amplitudes they are typically unstable). In this study, only one- and two-component DNVM are analyzed, they are reducible to the dynamical systems with one and two degrees of freedom, respectively. There exist 4 one-component and 12 two-component DNVM with in-plane atomic displacements. Any two-component mode includes one of the one-component modes. If the amplitudes of the modes constituting a two-component mode are properly chosen, periodic in time vibrations are observed for the two degrees of freedom at frequencies omega and 2 omega, that is, second harmonic generation takes place. For particular DNVM, the higher harmonic can have frequency nearly two times larger than the maximal frequency of the phonon spectrum of graphene. Excitation of some of DNVM results in the appearance of negative in-plane pressure in graphene. This counterintuitive result is explained by the rotational motion of carbon hexagons. Our results contribute to the understanding of nonlinear dynamics of the graphene lattice.