Theory of holey twistsonic media

Rotating two overlapping lattices relative to each other produces the well known moiré interference patterns and has surprisingly led to strongly correlated superconductivity in twisted bilayer graphene. This seminal effect that is associated with electrons occupying flat dispersion bands has stimulated a surge of activities in classical wave physics such as acoustics to explore equivalent scenarios. Here, we mimic twisted bilayer physics by employing a rigorous sound wave expansion technique to conduct band engineering in holey bilayer plates, i.e., twistsonic media. Our numerical findings show how one flexibly is able to design moiré sound interference characteristics that alone are controlled by the twist angle and the interlayer air separation. More specifically, our numerical approach provides a significant advantage in both computational speed and storage size in comparison with widely used commercial finite-element-method solvers. We foresee that our findings should stimulate further studies in terms of band engineering and exotic topological twisted phases.