Abstract
Zak phases in two types of acoustic metamaterials with negative density or negative modulus are studied. Different from phononic crystals based on Bragg scattering, extraordinary performance in acoustic metamaterials originates from local resonance. We find that the Zak phases in metamaterials are determined by the resonances of scatterers, side pipes, or membranes. Additionally, it is observed that the topological transition points, symmetrical properties of edge states, input impedances, and reflection phases in forbidden bands are all related to the resonances of the scatterers, and the relationship can be used to create surface states at the interface of two types of acoustic metamaterials.
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