Intrinsic Localized Modes in Anharmonic Lattices

Abstract

The success of the harmonic approximation in describing vibrations of condensed matter systems comes about because the plane wave amplitude at any particular site is extremely small hence it does not matter that the intermolecular potentials themselves are considered to be anharmonic in nature. Anharmonicity is generally introduced perturbatively to explain experimentally observed phenomena such as thermal expansion and phonon combination bands. Here we examine the dynamical properties of a locally excited anharmonic lattice such as might be expected to occur during an optical excitation of a coupled electron-lattice system so that the anharmonicity can play a more significant role. One development presented here is a straightforward demonstration of intrinsic localized modes in perfect one-dimensional monatomic lattices with quartic anharmonicity. These modes are similar to those associated with previously studied force constant defects, but they may be located anywhere in a perfect lattice and can actually move from site to site given the appropriate initial conditions. Associated with each localized vibrational mode in monatomic lattices with cubic and quartic anharmonicity is a localized dc distortion which forms an integral part of this new dynamical configuration. The softening of the potential with large displacements from equilibrium also produces a red-shift in the local mode frequency, but stable modes are observed in molecular dynamics simulations for a large range of anharmonicity parameters. The building blocks presented here for the development of localized modes in the one dimensional anharmonic chain can be used directly in the discussion of more complex nonlinear systems.KeywordsLocalize ModeStatic DisplacementBreathing ModeAnharmonic LatticeAnharmonicity ParameterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.