Topological elastic edge waves in two-dimensional continuum lattice

Abstract

In recent years, the topological edge mode, which has been actively studied in condensed matter physics, has received intense attention in classical wave mechanics because of its robust propagation against defects and sharp corners. In this work, we investigate the topological phase transition in continuum lattices and design an elastic topological edge waveguide. First, we show the topological phase transition in discrete hexagonal lattice associated with the intrinsic conic dispersion and spatial symmetry breaking, by deriving an effective dispersion model. It can be extended to the continuum lattice and offers design guides for topological elastic waveguides. Second, we propose an elastic waveguide using a continuum hierarchical hexagonal lattice by taking the notion of valley-dependent topological phase. We confirm the topological phases in the structures by numerically calculating the topological invariants, and we demonstrate that the valley Hall edge wave is robust to sharp bends using a time transient simulation. Lastly, we design a wave splitter and frequency filter by combining the lattice structures with gapped and gapless edge mode, which can be tuned by changing the geometric parameters. The proposed structure can be a practical design guide for elastic wave logic circuits and can widen the scope of multifunctional structures to include the topological phase.