Flat Band Engineering in Gigahertz Surface Acoustic Wave Metamaterials

Traditional metamaterials derive desired wave dispersion properties from the geometries of their primitive unit cells. In this work, we instead design a metamaterial whose functionality originates from coordinated variation of primitive unit cells within a supercell framework. We deposit gold microstructures on a lithium niobate substrate to control surface acoustic wave (SAW) propagation in the gigahertz regime. We produce a moiré framework that arises from spatially-encoded in-plane variation of microstructure parameters rather than the relative orientation of layers in a multilayer system. We characterize our device using complementary transmission measurements and direct imaging of frequency-dependent SAWs. Our metamaterial hosts isolated flat bands, which have potential applications as high quality factor resonators for gigahertz technologies. By exploiting the analogy between the acoustic wave equation and the Schrödinger equation for electron propagation in a crystal lattice, our engineered acoustic flat bands may provide insight into their quantum counterparts.