Abstract
Roton dispersion relations have been restricted to correlated quantum systems at low temperatures, such as liquid Helium-4, thin films of Helium-3, and Bose–Einstein condensates. This unusual kind of dispersion relation provides broadband acoustical backward waves, connected to energy flow vortices due to a “return flow”, in the words of Feynman, and three different coexisting acoustical modes with the same polarization at one frequency. By building mechanisms into the unit cells of artificial materials, metamaterials allow for molding the flow of waves. So far, researchers have exploited mechanisms based on various types of local resonances, Bragg resonances, spatial and temporal symmetry breaking, topology, and nonlinearities. Here, we introduce beyond-nearest-neighbor interactions as a mechanism in elastic and airborne acoustical metamaterials. For a third-nearest-neighbor interaction that is sufficiently strong compared to the nearest-neighbor interaction, this mechanism allows us to engineer roton-like acoustical dispersion relations under ambient conditions.
Highlights
Roton dispersion relations have been restricted to correlated quantum systems at low temperatures, such as liquid Helium-4, thin films of Helium-3, and Bose–Einstein condensates
Based on a prediction by Landau[2] and following a suggestion by Feynman[3,4], the roton dispersion relation for longitudinal acoustical waves was observed in liquid Helium-4 at low temperatures by means of inelastic neutron scattering[5,6,7]
The first Brillouin zone is given by wavenumber jkj π=a. b Dispersion relation ωðkÞ 1⁄4 ωðÀkÞ
Summary
Roton dispersion relations have been restricted to correlated quantum systems at low temperatures, such as liquid Helium-4, thin films of Helium-3, and Bose–Einstein condensates. Mechanisms such as ordinary Bragg reflection[26,27], local resonances[28,29,30,31], near-ideal joints[32,33,34] introducing soft modes, spatial or temporal symmetry breaking[35,36,37,38], topology[39,40], duality[41,42], as well as geometrical nonlinearities[34,43] have independently given rise to a wealth of other unusual dispersion relations and quasi-static behaviors of elastic and acoustical metamaterials. We apply the same concept to airborne acoustical waves in macroscopic three-dimensional channel-based metamaterials to illustrate the general nature of the approach
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