Coherent phonon scattering by geometric defects in a planar quantum waveguide

Using the spring-mass model and a matching method formalism, we investigate the scattering of acoustic phonons by a geometric defect (step) in a planar quantum waveguide. The mono-atomic step is treated as the perturbed interface between two single semi-infinite atomic layers occupying the half spaces on either side of the step. In fact the planar waveguide is an isolated step in the direction perpendicular to the plan. As in the electronic case, the transmission coefficients are characterized by strong asymmetrical resonances, identified as Fano-like resonances, due to the degeneration of the localized states induced by the step and those of the propagation continuum. Whereas the interferences between diffused and reflected waves in the perturbed step region generate Fabry–Pérot oscillations. The resulted transmission and conductance spectra can thus be regarded as identifying features and may therefore be used for their characterization. The results could also be useful for controlling thermal conductance artificially and the design of phonon devices. To illustrate the method, a detailed discussion of the transmission spectra is presented for different geometries in the null and oblique incidence cases.