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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.

Dark state, zero-index and topology in phononic metamaterials with negative mass and negative coupling