Surface Phonons and Other Localized Excitations

摘要

The diatomic linear chain of masses coupled by harmonic springs is atextboook model for vibrational normal modes (phonons) in crystals. In additionto propagating acoustic and optic branches, this model is known to support a``gap mode'' localized at the surface, provided the atom at the surface haslight rather than heavy mass. An elementary argument is given which explainsthis mode and provides values for the frequency and localization length. Byreinterpreting this mode in different ways, we obtain the frequency andlocalization lengths for three other interesting modes: (1) the surfacevibrational 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 monatomicchain.