Dirac cones and topological torsional modes in phononic nanowires using Su-Schrieffer-Heeger Model

Topological materials have attracted significant attention due to their distinct edge states, known for their robustness to local perturbations. In the field of phononic crystals, these states manifest as topological surface or interface modes, offering promising applications in waveguiding and energy harvesting. This study explores the emergence and control of azimuthal symmetric torsional interface states in phononic nanowires (PNWs) composed of alternating cylindrical layers. In the framework of the Su-Schrieffer-Heeger (SSH) model, we use the Green's function approach to derive analytical expressions of the dispersion relations to predict all Dirac-point positions and interface modes. The analytical results are confirmed by finite element method simulations performed using COMSOL Multiphysics. In PNWs with symmetric unit cells, band-structures and scattering calculations reveal tunable interface modes whose frequencies and propagation characteristics can be adjusted via geometrical parameters. We also demonstrate through Zak-phase, local density of states (LDOS), and transmission-spectrum analyses that these interface states remain fixed and topologically protected under variations of the dimerization parameter. These findings pave the way for exploiting topological interface states in PNWs, thus opening to innovative phononic devices and contributing to the advancement of the field of topological physics.