A calculation of the phonon contribution to the coherent transport between two-dimensional (2D) lattices is presented in this paper. The model structure is obtained by the juxtaposition of semi-infinites square ([Formula: see text] and triangular ([Formula: see text] leads, which thus define the nanojunction [Formula: see text]/[Formula: see text] and its inverse [Formula: see text]/[Formula: see text]. We determine, numerically and by simulation, the 2D interface observables for different values of masses and elastic coupling in the nanojunction zone. The local dynamics and atomic nanojunction response to the microscopic changes, in the interfacial domain, are subjects to our investigation. The theoretical formalism based on the matching technique is applied to describe the lattice dynamics and the evanescent phonon modes, in the two studied 2D interfaces. We mainly analyze the vibration spectra, the coherent phonon transmission/reflection and the phononic transmittance through the interface, as elements of a Landauer–Büttiker type scattering matrix. The obtained results show that the nanojunction domain is an effective phonon splitter and suggest that its characteristics may be controlled by varying its nanometric parameters. The observed fluctuations are due to the coherent coupling between continuum modes and the phonons’ discrete states induced by the connected atomic sites.
On star-convex volumes in 2-D hydrodynamical flows and their relevance for coherent transport
