Abstract
This work presents a theoretical approach for the study of phonon dynamics and scattering properties of an infinite linear atomic chain perturbed by a mono atomic step. The coherent transmittance scattering cross-sections for incident phonons on the atomic waveguide structure are calculated using the Landauer-Buttiker electron scattering description and the matching method formalism with the nearest and next nearest neighbour interactions. Numerical results for different configurations yield an understanding of the chain dynamical properties and the effects on phonon transmittance due to incoming phonons. The reflectance and transmittance coefficients show spectral characteristic features depending on the cut-off frequencies for the propagating phonons. They illustrate the occurrence of Fano resonances in the scattering spectra that result from degeneracy of step localized modes and propagating continuum modes due to the breakdown of the translation symmetry in the propagating direction. Furthermore, the interferences between diffused and reflected waves in the step regions generate Fabry-Perot oscillations whose number is determined by the distance between steps and the number of terraces.
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