Abstract
Phononic metamaterials have attracted extensive attention since they are flexibly adjustable to control the transmission. Here we study a one-dimensional phononic metamaterial with negative mass and negative coupling, made of resonant oscillators and chiral couplings. At the frequency where the effective mass and coupling are both infinite, a flat band emerges that induces a sharply high density of states, reminiscent of the phononic dark states. At the critical point of band degeneracy, a phononic Dirac-like point emerges where both the effective mass and the inverse of effective coupling are simultaneously zero, so that zero-index is realized for phonons. Moreover, the phononic topological phase transition is observed when the phononic band gap switches between single mass-negative and single coupling-negative regimes. When these two distinct single negative phononic metamaterials are connected to each other, a phononic topological interface state is identified within the gap, manifested as the phononic counterpart of the topological Jackiw–Rebbi solution.
Highlights
Metamaterials usually exhibit extraordinary properties that can not found in nature like the negative permittivity (ε), negative magnetic permeability (μ) of electromagnetical metamaterials which can realize reversed Doppler effect, reversed Cherenkov radiation and negative refraction index [1,2,3,4,5,6]
With the development of the theory, the negative modulus is demonstrated [13] by the array of subwavelength Helmholtz resonators or side holes on a tube [14] and the negative mass is realized by membrane-type acoustic tube [15] in low frequency range
The blue area is caused from Bragg scattering it is in double negative range and yellow areas correspond to the band gap induced by the single negative properties, which means that in the process of wave propagation, the wave present an evanescent wave of exponential decay leading to the vanishing transmittance within a certain frequency range
Summary
Metamaterials usually exhibit extraordinary properties that can not found in nature like the negative permittivity (ε), negative magnetic permeability (μ) of electromagnetical metamaterials which can realize reversed Doppler effect, reversed Cherenkov radiation and negative refraction index [1,2,3,4,5,6]. The double negative parameters in the structure with array of periodic thin membranes and side holes [16] are proposed. The mass-spring structure with different coupling and spatial distribution can have negative effective parameters [21,22,23,24,25,26,27] because of Bragg scattering and resonant mechanism in different frequency regimes. There are many other properties of phononic metamaterials attracting increasing interest recent years, such as the zero refraction index (zero-index for short) and topological bands. We show that by design, the oscillator mass and inter-oscillator coupling, both are positive naturally, can be either single negative or double negative effectively within a certain frequency range. A topological interface state is identified between two different single negative phononic materials
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