Surface Phonons and Other Localized Excitations

TL;DR

This paper analyzes localized vibrational modes in a diatomic chain, explaining surface and impurity modes, providing explicit frequencies and localization lengths, and offering insights into various surface and impurity-related excitations.

Contribution

It introduces a simple explanation for surface localized modes and derives their properties for different impurity and stacking fault configurations.

Findings

Surface gap mode exists for light surface atoms.

Localized impurity modes have specific frequencies and localization lengths.

The model explains various surface and impurity vibrational excitations.

Abstract

The diatomic linear chain of masses coupled by harmonic springs is a textboook model for vibrational normal modes (phonons) in crystals. In addition to propagating acoustic and optic branches, this model is known to support a ``gap mode'' localized at the surface, provided the atom at the surface has light rather than heavy mass. An elementary argument is given which explains this mode and provides values for the frequency and localization length. By reinterpreting this mode in different ways, we obtain the frequency and localization lengths for three other interesting modes: (1) the surface vibrational mode of a light mass impurity at the surface of a monatomic chain; (2) the localized vibrational mode of a stacking fault in a diatomic chain; and (3) the localized vibrational mode of a light mass impurity in a monatomic chain.