Vibrational Properties of Two Isolated Steps: A Theoretical Model

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.

Dynamical Properties of the Interface Between Two Thin Films

“…15 The experimental evidence that demonstrates the localized phonons on the step edges of vicinal Ni (977) surface was observed using helium-atom scattering 16 and was addressed by Niu et al 17 Recently, we have theoretically treated the dynamical properties of quasi-low-dimensional structure consisting of two monoatomic steps at the interface between three coupled semi-infinite and single semi-infinite atomic layers. 18 Results of which were in qualitative agreement with previous works [19][20][21] and demonstrated that the breakdown of translational symmetry normal to the step edges give rise to several branches parallel to them.…”

Scattering and Transmission of Elastic Waves from an Interface Between Two Planar Waveguides

“…For surface with inhomogeneities such as two isolated steps, the problem has been recently addressed. 24 The breakdown of translational symmetry perpendicular to the steps edges gives rise to several Rayleigh-like branches localized in the neighborhood of the steps. We apply this procedure for the two-dimensional systems in the neighborhood of inhomogeneity, such as an interface extending from the boundary into the right and left domains of a perfect waveguide, in order to derive a unique solution for the commensurate evanescence of localized vibrational states in two dimensions near the interface.…”