Emergence of exceptional points and skin modes in non-Hermitian one- and two-dimensional phononic structures

This study investigates the emergence of exceptional points and skin modes in non-Hermitian phononic structures through numerical analysis based on the finite element method and tight-binding models. A one-dimensional phononic structure was designed by combining aluminum beams, plastic necks, and tungsten columns, where non-reciprocal coupling and damping were introduced to realize non-Hermitian characteristics. The eigenfrequencies and mode shapes were evaluated under periodic boundary conditions, demonstrating the emergence of exceptional points characterized by the coalescence of the real part of the eigenvalues. In addition, localization of vibrational energy in specific regions was achieved, indicating the presence of skin modes even in periodic structures. Furthermore, as an initial step toward extending this analysis to two-dimensional systems, a supercell model was analyzed using a tight-binding model, in which four-site unit cells were arranged on a square lattice. Exceptional points were successfully observed even in a supercell consisting of 16 sites. These findings suggest that exceptional points and skin modes can also emerge in two-dimensional non-Hermitian periodic structures, providing a design guideline for controlling the spatial distribution of energy.