Abstract
We investigate the dynamical properties of two isolated steps on the surface. We present the solution of the full dynamical problem arising from the absence of translation symmetry in two dimensions due to extended surface steps on the surface boundary of an insulating substrate. The calculations concern in particular the dynamics of localized modes of an atomic step on the surface of a cubic lattice. The theoretical approach determines the vibrational field in both steps. The matching method, which constitutes a powerful formalism for determining the vibrational properties of such disordered surfaces, is used. The model presented in this study consists of two monatomic steps as the interface between three coupled semi-infinite and single semi-infinite atomic layers. The dynamical properties of the perfect waveguides are presented and calculated numerically. The breakdown of translational symmetry perpendicular to the step edges gives rise to several Raleigh-like branches localized in the neighborhood of the steps. Typical dispersion curves for these modes along the steps are given with their polarization.
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