Topological edge states in phononic plates with embedded acoustic black holes

Abstract

We report on the design of phononic plates based on a periodic lattice of acoustic black holes (ABH) and capable of supporting topological edge states. The design is based on the established concept of the acoustic valley Hall effect (AVHE) that is the elastic analogue of the quantum valley Hall effect (QVHE) for quantum mechanical systems. The basic structure consists of a triangular lattice of circular ABHs whose symmetry guarantees the existence of Dirac dispersion at the corners of the Brillouin zone. Starting from this symmetric lattice, space inversion symmetry (SIS) can be broken by introducing an angle-dependent scaling of the ABH taper profile. Depending on the sign of the scaling factor, two topologically distinct lattice configurations can be obtained and assembled in order to create a domain wall characterized by unconventional dynamic properties. More specifically, such domain wall supports the formation and propagation of quasi-unidirectional elastic guided modes that are topologically protected against back-scattering due to impurities or defects in the lattice.