Zero refractive index in time-Floquet acoustic metamaterials

New scientific investigations of artificially structured materials and experiments have exhibited wave manipulation to the extreme. In particular, zero refractive index metamaterials have been on the front line of wave physics research for their unique wave manipulation properties and application potentials. Remarkably, in such exotic materials, time-harmonic fields have an infinite wavelength and do not exhibit any spatial variations in their phase distribution. This unique feature can be achieved by forcing a Dirac cone to the center of the Brillouin zone (⁠$Γ$ point), as previously predicted and experimentally demonstrated in time-invariant metamaterials by means of accidental degeneracy between three different modes. In this article, we propose a different approach that enables true conical dispersion at $Γ$ with twofold degeneracy and generates zero index properties. We break time-reversal symmetry and exploit a time-Floquet modulation scheme to demonstrate a time-Floquet acoustic metamaterial with zero refractive index. This behavior, predicted using stroboscopic analysis, is confirmed by full-wave finite element simulations. Our results establish the relevance of time-Floquet metamaterials as a novel reconfigurable platform for wave control.