Simulating twistronics in acoustic metamaterials

Abstract Twisted van der Waals 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 perfectly replicates the band structures of its quantum counterpart, including mode localization at a magic angle of 1.12 ∘ . By tuning the thickness of the interlayer membrane, we reach a regime of strong interlayer tunneling where the acoustic magic angle appears as high as 6.01 ∘ , equivalent to applying 130 GPa to twisted bilayer graphene. In this regime, the localized modes are over five times closer together than at 1.12 ∘ , increasing the strength of any emergent non-linear acoustic couplings.