Subwavelength and directional topological waveguides in thin plates using Pseudo spin Hall Effect

Inspired by the discovery of topological insulators, it is recent that the underlying topological framework is being used to design artificial structures, the so-called topological metamaterials, with the aim of controlling the flow of photons and phonons on their boundaries. In this regard, tailoring elastic waves in mechanical structures shows tremendous potential for engineering usages, such as novel sensing, energy harvesting, and impact mitigation purposes. Here, we propose a macro-scale, continuum structure to mimic pseudo spin Hall Effect at a subwavelength scale and achieve a robust and directional control of elastic waves along a designed waveguide. This structure consists of a thin continuum plate with local resonators mounted on its top. Using the plane wave expansion method and the finite element method, we show the existence of a double Dirac cone in the dispersion at low frequencies. We show that by modifying the design strategically, we can open a gap at the Dirac frequency and also achieve band inversion in the system. When two topologically distinct systems are placed adjacently, we show the existence of two pseudo-spins propagating in opposite directions at the domain wall.