Acoustic metamaterials with spinning components

We show that an acoustic metamaterial consisting of an array of spinning cylindrical inclusions can possess many unusual properties, including folded bulk bands and interface-state bands. The folding of bands inside the first Brillouin zone is made possible by a rotation-induced antiresonance of compressibility and the rotational Doppler effect. Both bulk and interface-state band dispersions exhibit remarkable filling-fraction-dependent features such as the emergence of a cutoff frequency when the filling fraction exceeds a critical value. Robust one-way transport properties are supported by nondegenerate interface states, but within the same band, interface states at different frequencies can have different propagation directions.