Simulating twistronics in acoustic metamaterials

Twisted van der Waals (vdW) heterostructures have recently emerged as a tunable platform for studying correlated electrons. However, these materials require laborious and expensive effort for both theoretical and experimental exploration. Here we numerically simulate twistronic behavior in acoustic metamaterials composed of interconnected air cavities in two stacked steel plates. Our classical analog of twisted bilayer graphene (TBG) perfectly replicates the band structures of its quantum counterpart, including mode localization at a magic angle of 1.12º. However unlike the quantum counterpart, we can simply and continuously tune the thickness of the interlayer membrane to reach a regime of strong interlayer tunneling where the acoustic magic angle appears as high as 6.01º, equivalent to applying 130 GPa to twisted bilayer graphene. In this regime, the localized modes are over five times closer together than at 1.12º, increasing the strength of any emergent non-linear acoustic couplings. Currently, our tunable metamaterial design will allow simulation of a broad class of twisted vdW heterostructures at accessible moiré unit cell sizes. In the longer term, 3D-printed acoustic metamaterials could offer a new way to experimentally simulate complex, multilayer vdW heterostructures with overlapping moiré patterns that exceed all computational capabilities.