Band Gap Engineering and Microscopy in LiNbO3 Surface Acoustic Wave Metamaterials

We report direct, frequency-dependent imaging of surface acoustic waves (SAWs) in lithium niobate (LiNbO3) metamaterials. Based on the analogy between the acoustic wave equation and the Schrodinger equation, these metamaterials serve as a platform to rapidly prototype and characterize 2D quantum materials. By depositing a periodic array of metallic microstructures on LiNbO3, we control SAW propagation, simulating the electronic dispersion of materials with similar lattice geometry. Previous direct visualization of traveling SAWs by laser scanning vibrometry is limited to micron-scale spatial resolution, while microwave impedance microscopy (MIM) is limited to very narrow frequency ranges. Here, we introduce the use of electrostatic force microscopy (EFM), which achieves sub-micron resolution over a broad bandwidth exceeding 600 MHz. We map the SAW band structure of graphene-like metamaterials, including a Dirac cone at the K point. Additionally, we observe a tunable band gap induced by broken sub-lattice symmetry in metamaterial analogs of hexagonal boron nitride (h-BN). Our technique facilitates faster and more detailed studies of complex SAW metamaterials and, more broadly, enhances the experimental toolkit for band engineering platforms.