Interference effects in phonon scattering across a double atomic well

We develop an analytical and numerical formalism to study the double atomic nanowell configuration influence on coherent transmission and reflection scattering, derived as elements of a Landauer-Büttiker type scattering matrix in quasi-one-dimensional multichannel waveguides. The state densities at neighbourhood of the defect region are investigated. The defect region consists in the presence of a double atomic nanowell occurring in thin film. One solves this problem by the matching method in the harmonic approximation. The theoretical formalism using simultaneously the Green's function and the matching method is detailed in order to describe the complete evanescent and the propagating fields. The phononic coherent conductance is also studied. Numerical calculations are presented and illustrated as function of the force constants occurring in the model. The fluctuations in the conductance spectra are related to Fano resonances due to the coherent coupling between travelling phonons and the localized vibration modes in the neighbourhood of the nanowell domain.