Coherent Ballistic Phononic Transport at Slab Nanostructure in Surface Crystalline

We investigate the scattering phenomenon at the non-uniform crystalline surface. The breakdown of translation symmetry caused by inhomogeneity gives rise to localized modes un its vicinity. The Newton equation and matching technique are used to study the phonon scattering mechanisms at the inhomogeneity. Together with the determination of the transmission and reflection probabilities and the elastic wave average transmittance across the defect, numerical results are presented over a broad range of scattering energies. This illustrates the differences in the scattering spectra of the softening, homogeneity, and hardening features of the perturbed defect. The coherent coupling between the propagating mode of the ideal waveguide and the localized modes formed by the defect results in fano resonances in the spectra. A detailed explanation is provided for a range of values of the elastic constants in the bulk and inhomogeneous domain. The system conductance is computed using the stimulating dimensionless frequencies and the characteristics of the system model.