Reconfigurable elastic quantum valley Hall edge states in a piezoelectric topological metamaterial

摘要

Unlike conventional elastic waveguides, topologically protected wave transmission in topological metamaterials is immune to backscattering and localization from lattice imperfections and sharp corners. Topologically protected waveguides can be formed by breaking space inversion symmetry within the unit cell of a hexagonal lattice, creating an elastic realization of the quantum valley Hall effect. Recent studies have demonstrated the achievement of tunable topological edge states through the application of an external bias, such as a mechanical, thermal, or magnetic load. These initial studies demonstrate the capability to modify topological edge states through oftentimes complex realizations of truss-like lattice structures or external stimuli. However, a comprehensive reconfigurable topological metamaterial that enables real-time adaptation of both frequency and spatial characteristics of topological properties in an easily integrable manner has yet to be developed. Thus, to advance the state of the art, this research introduces an electromechanical metamaterial with the capability to adjust the frequency range for topological edge states and instantaneously create or eliminate topological interfaces through the integration of piezoelectric circuitry with a continuous mechanical substrate. The metamaterial is comprised of inductor circuitry connected to a thin piezoelectric plate in a periodic manner which produces a hexagonal lattice pattern of electromechanical resonators. The plane wave expansion method is used to reveal a tunable Dirac cone in the band structure of the lattice unit cell and indicate how perturbations to the circuit inductance can open topologically distinct bandgaps. Numerical simulations identify edge modes located at frequencies within the topological bandgap and demonstrate adaptive topologically protected elastic wave transmission.