Harmonic Oscillator States in Acoustic Twisted Bilayer Graphene*

The discovery of twisted van der Waals heterostructures hosting moiré lattices has opened a parameter space of materials and twist angles too vast for direct exploration. Acoustic metamaterials can be used to mimic the behaviors of quantum materials, serving as cheap and rapid prototypes for their expensive and laborious quantum counterparts. For example, twisted bilayer graphene (TBG) has already been successfully translated into the field of acoustics [1]. While TBG is known to feature isolated flat bands due to the hybridization of dispersive Dirac states, it is also possible to manifest a ladder of flat band harmonic oscillator states originating at the parabolic band edges farther from the Fermi level [2]. Using COMSOL Multiphysics, we discover emergent harmonic oscillator modes in acoustic twisted bilayer graphene, and we simulate their real space distribution. The twist angle and interlayer coupling strength of our metamaterial can be easily tuned to control the energy spacing of the flat bands and their localization across the moiré lattice supercell. Our metamaterial may serve as a tunable platform for emergent phenomena such as second harmonic generation.