Topological edge states in acoustic Kagome lattices

We demonstrate that an acoustic Kagome lattice formed by an array of interconnected resonant cavities exhibits a new class of topological states protected by C ₃ symmetry, and it is characterised by a topological invariant in the form of a winding number in Pauli vector space. This acoustic topological metamaterial can be considered as the two-dimensional analogue of the Su–Schrieffer–Heeger model, exhibiting a topological transition when a detuning is introduced between the inter-cell and intra-cell hopping amplitudes. The topological transition caused by such detuning is accompanied by the opening of a complete topological band gap, which may host edge states. The edge states emerge on either truncated ends of the lattice terminated by a cladding layer or at the domain walls between topologically nontrivial and trivial domains. First-principles simulations based on full-wave finite element method are used to design the lattice and confirm our analytical predictions.