Phonons on stepped surfaces

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Abstract
A simple model of fcc lattice dynamics is studied in the vicinity of a clean, unreconstructed, high-Miller-index (i.e., stepped) surface. Depending on the vibrational modes’ spatial extent, they are classified as either bulk phonons, surface phonons, or step phonons. The existence and characteristics of the latter class of vibrational modes are presented throughout the (one-dimensional) step Brillouin zone (BZ). Five classes of stepped surfaces are examined, each differing in the Miller indices of the terrace [(111) or (100)] and step face [(111), (100), or (110)]. All but one of the systems exhibit modes truly localized to the edge. There are many similarities to the study of surface phonons. For instance, when degenerate with the bulk- or surface-phonon bands, the step phonons acquire a finite lifetime and become step resonances. A total of seven step phonons and four step resonances are seen. Most of these are strongly localized to the edge only near the end of the step BZ. Unlike regular surface modes, the step-phonon characteristics (frequency, polarization, and amplitude) depend sensitively on the interatomic potentials near the steps. Two step-phonon measurements have yielded information about these important step parameters. Using a crude estimate of the inelastic-scattering intensity, I propose the possibility for a similar experiment with Ni(755) using existing techniques.