Transverse intrinsic localized modes in monatomic chain and in graphene

• In a stretched monatomic chain, long-living nonlinear transverse localized modes may exist.
• Transverse vibrations of a chain slowly decay due to creation of longitudinal phonons.
• Lifetime of transverse vibrations of a chain may exceed billion periods of vibrations.
• In stretched graphene, long-living out-of-plain localized vibrations may exist.

In this paper an analytical and numerical study of anharmonic vibrations of monatomic chain and graphene in transverse (perpendicular) with respect to the chain/plane direction is presented. Due to the lack of odd anharmonicities and presence of hard quartic anharmonicity for displacements in this direction, there may exist localized anharmonic transverse modes with the frequencies above the spectrum of the corresponding phonons. Although these frequencies are in resonance with longitudinal (chain) or in-plane (graphene) phonons, the modes can decay only due to a weak anharmonic process. Therefore the lifetime of these vibrations may be very long. E.g. in the chain, according to our theoretical and numerical calculations it may exceed 1010 periods. We call these vibrations as transverse intrinsic localized modes.