Transmission of longitudinal phonons through a mass-spring nanoring

Abstract

In this paper, we study the coherent phonon transport through a cyclic mass-spring structure which is embedded between two longitudinal phononic leads within the harmonic approximation. We assume only the in-plane vibrations for the atoms of the structure and also the nearest neighbor interaction between them. By starting from the system potential energy and then using the Green's function method, we construct a formalism to compute the phononic transmission coefficient and density of states/modes of the system. The numerical calculations are performed for a hexagonal mass-spring ring in the presence and absence of a massive impurity. The results reveal that, the variation of value of the masses or spring constants in the ring leads to appearance of the Fano resonance in the transmission spectrum. This phenomenon occurs at a special phonon frequency independent of the impurity position in the structure.