We introduce a new class of tunable periodic structures formed by launching two obliquely propagating surface acoustic waves on a piezoelectric substrate that supports a two-dimensional material. The resulting acoustoelectric superlattice exhibits two salient features. First, its periodicity is widely tunable, spanning a length scale intermediate between moiré superlattices and optical lattices, enabling the formation of narrow, topologically nontrivial energy bands. Second, unlike moiré systems, where the superlattice amplitude is set by intrinsic interlayer tunneling and lattice relaxation, the amplitude of the acoustoelectric potential is externally tunable via the surface acoustic wave power. Using massive monolayer graphene as an example, we demonstrate that varying the frequencies and power of the surface acoustic waves enables in situ control over the band structure of the 2D material, generating flat bands and nontrivial valley Chern numbers, featuring a highly localized Berry curvature.

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• Electronic structure
• Topological materials
• Surface acoustic wave