Intrinsic Localized Vibrational Modes in Anharmonic Crystals

Abstract

An intrinsic localized vibrational mode is shown to appear in a pure anharmonic crystal lattice with quartic anharmonicity. This is a discrete-space-version of a spatially localized configuration in nonlinear field theory. Two types of quartic anharmonic potential, optical-mode-type and acoustical-mode-type, are considered to illustrate the existence of an s-like localized mode in a simple cubic lattice with nearest neighbour interactions. The calculation is done by using the lattice Green's function formalism in close analogy with the case of a localized mode due to an impurity atom in the harmonic lattice and by solving a nonlinear eigenvalue problem with widely spread defect space in a successive manner. It is shown that such an intrinsic localized mode can appear at any lattice site if the anharmonicity is sufficiently strong. The linear stability analysis of the localized mode is made to show that a localized mode lying above the top of the phonon frequency band is always stable. A brief study is also made on the movability of such an intrinsic anharmonic localized mode