Abstract
A nonlinear vibration mode, referred to as the intrinsic localized mode (ILM), in graphene is investigated based on precise numerical solutions obtained by the iteration method coupled with molecular dynamics simulations. We obtain ILMs for which the frequency is greater than the maximum frequency of the phonon bands of graphene. The amplitude and structure of ILMs indicate that these ILMs are simply vibration modes due to the nonlinearity of the system. Moreover stability analysis of ILMs in graphene is performed numerically by solving the eigenvalue problem of the monodromy matrix based on Floquet theory for periodic solutions. In all cases, the ILM was found to have unstable perturbation modes. The growth rate of the unstable perturbation modes exhibits complex change behavior as the period of ILMs changes. The structure and growth rate of the unstable perturbation modes can be classified into two types. The most unstable perturbation mode is also localized and provides cooperative motions of neighbor atoms of the ILM.
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