Topological one-way edge states in locally resonant metamaterials

The quantum anomalous Hall effect (QAHE) enables dissipation-free motion within its edge states, offering considerable potential for developments in the fields of electronics, phononics, and elastic waves. In this study, we introduce an elastic metamaterial designed to realize the QAHE at low frequencies. Our approach involves deploying a two-dimensional honeycomb spring-mass system on a rotating platform to break time-reversal symmetry via the Coriolis Force and incorporating local resonators to achieve low-frequency topological edge states. We begin by deriving the system’s equations of motion through analytical rigid body dynamics. Subsequently, we apply Bloch wave solutions to establish the dispersion relations and identify the topological edge states. We then conduct numerical simulations to confirm the one-way transmission characteristics of these states. The addition of local resonators not only extends the frequency range of the topological edge states but also lowers the operational frequency of the system. This robust waveguide, capable of one-way transmission, has potential applications in directional transmission, vibration damping, noise reduction, and acoustic imaging.