Cubic-symmetry acoustic metamaterials with roton-like dispersion relations

In our previous work, we have shown that nonlocal interactions in acoustic metamaterials can lead to highly unusual roton-like dispersion relations exhibiting a minimum of frequency versus wavenumber similar to that of superfluid Helium-4. However, this behavior was limited to only one or two propagation directions of sound. Here, we design a three-dimensional cubic-symmetry airborne acoustic metamaterial with nonlocal interactions along three orthogonal directions. By using numerical finite-element calculations, we show that the metamaterial supports roton-like behavior along all three orthogonal directions, but the behavior is far from isotropic. We compare these calculations with a simplified semi-analytical model, leading to good overall agreement. Corresponding experiments appear in reach, but are demanding due to the required dense and complex three-dimensional network of acoustic channels that connect compartments of air.