Phonon transport in extended harmonic square mass-spring nanoribbons: Influence of second-neighbor interactions

In this paper, we present a semi-analytical method employing the Green’s function technique to compute the phonon transmission coefficient in a two-dimensional square mass-spring network under the harmonic approximation. The structure includes a small region in the center where second-neighbor springs are introduced. We perform a unitary transformation on the system’s dynamic matrix to separate the phonon modes in the structure’s vertical direction. This approach simplifies the semi-infinite sections (phonon leads) into basic mass-spring chains with generalized dispersion relations. Consequently, the inverse of the Green’s function matrix of the transformed central part is constructed and numerically inverted. Our numerical analysis of phonon transport in a long, narrow square nanoribbon reveals that the inclusion of stronger vertical springs in a small region significantly suppresses the phonon transmission coefficient and opens a frequency gap in the center of the low-frequency band. Interestingly, in contrast to the resonant regime, the presence of diagonal springs in the perturbed region enhances tunneling phonon conductance.