PACS. 61.46.+w Clusters, nanoparticles, and nanocrystalline materials, 61.12.Bt Theories of diffraction and scattering, 68.65.+g Low-dimensional structures (superlattices, quantum well structures, multilayers): structure, and nonelectronic properties,
The scattering of phonons in two-dimensional hexagonal crystals at their defect boundaries are investigated. These so-called Wigner crystals exist in different monolayer and bilayer forms and present a rich variety of defect boundaries. To fix the calculation we investigate phonon scattering for the physisorbed monolayers on solid surfaces, that exhibit two types of domain boundaries called heavy and superheavy solitons delimiting the crystalline ordered phase domains. A detailed study is presented for the reflection and transmission of the two-dimensional 2D crystal phonons at these domain boundaries, where the scattering spectra are related to the change of their elastic constants. Fano resonances may appear in the phonon transmission spectra due to the coherent coupling between the 2D crystal phonons and the localised vibration modes on the domain boundary. For a resonator cavity made up of two such domain boundaries, additional Fabry-Perot oscillations are found in the scattering spectra.
The influence of a special class of atomic nanostructures embedded on a waveguide is analyzed for the scattering and transmission of elastic waves in quasi-one-dimensional multicanal waveguides. The quasi-one-dimensional waveguide is constructed of double chains of atoms, and the nanostructures consist of geometrical configurations, where the double chains are arranged to form several types of double L-shaped joints. Numerical results are presented for the three types of nanostructures, using the matching method. The theoretical approach allows us to calculate the reflection and the transmission probabilities as well as the average phonon conductance of the system along the waveguide. The results show that the transmission probabilities and the average conductance depend strongly on the type of geometrical joint nanostructure. The pronounced fluctuations in the transmission and conductance spectra as a function of the frequency can be understood as Fano resonances that result from the coherent coupling between the propagating modes and the localized vibrational modes induced by the nanostructures.
A theoretical model is presented for the study of the scattering of phonons at an extended inhomogeneous boundary separating thin solid monatomic films. The model system consists of two solid films with otherwise stress-free surfaces on either side of an atomic well boundary. The coherent reflection and transmission scattering cross sections for phonons incident from the interior of the thin films on the inhomogeneous atomic well boundary are calculated in accordance with the Landauer-Büttiker coherent scattering description, using the matching method with nearest and next-nearest neighbor elastic force constants. This is done specifically for two different cases of elastic interactions on the boundary to investigate the consequences of their softening and hardening for the coherently scattered spectra. The numerical results yield an understanding for the effects on coherent phonon conductance due to phonon incidence and to the elastic nature of the boundary. The coherent reflection and transmission scattering cross sections show characteristic spectral features that are invariant with the change of the boundary force constants, depending solely on the cutoff frequencies for the propagating phonons and on incidence angle. They also show the Fano resonances that result from the interactions of propagating phonons with the localized vibrational Rayleigh-like modes on the boundary, depending on the boundary elastic force constants. The evolution of the system average conductance per phonon mode with incidence illustrates an interesting effect. An experimental observable this average conductance remains constant at half a phonon in intensity over significant frequency intervals. The effect is remarkable inasmuch as it permits in principle the possibility of a constant intensity phonon source.
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