Surface localized modes in anharmonic systems at low dimensionality

In this paper we discuss in detail the localized vibrational modes in monoatomic and diatomic one-dimensional chains induced by anharmonicity. Analysis of the effects of the quartic anharmonic interactions in the Vibrational spectrum shows, in the monoatomic case, the appearance of surface modes, not allowed in the harmonic field, and of high-frequency modes. In the diatomic case we found two types of surface mode, the first reminiscent of the harmonic one and the second entirely due to the anharmonicity, and two localized gap modes arising from the top of the acoustic branch with odd parity centered on a heavy atom and even parity centered on a light atom. The introduction of cubic anharmonicity produces odd and even gap localized modes arising from the bottom of the optical branch and affects the surface modes.