Effect of anharmonicity on local defect modes in a one-dimensional crystal

The effect of anharmonicity on the vibrational modes of an isotopic defect in a one-dimensional chain is considered. It is shown that the anharmonicity causes some qualitative changes in the vibrational modes of the isotope. In particular, modes localized close to the defect with frequencies close to the lower edge of the spectrum can exist for both signs of the defect mass. A similar situation also holds for modes whose frequencies are localized near the upper edge of the harmonic approximation spectrum. It is shown that when anharmonicity is taken into account the modes become quasilocal.

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