Chern insulators, distinguished by a nonzero Chern number in topological phases, exhibit a quantum Hall effect without requiring Landau levels. Although acoustic counterparts of Chern insulators were created via engineered nonreciprocity with vortex flows, the concerning studies primarily relied on quantum-mechanical analogies, and full-wave simulations and experiments, which lack a theoretical model on the basis of the acoustic foundation. Thus, in this work, we present a theory to study acoustic Chern insulators (ACIs) created by introducing vortex flows into honeycomb lattices and derive an analytic solution for the Hamiltonian of the system from fundamental acoustic wave equations. The frequency band calculated using our theoretical model is in good agreement with that obtained using full-wave simulations, which demonstrates the accuracy of the theory. According to the theory, a different edge state is observed. Furthermore, the theory can also be applied to study the frequency band of deformed lattices, which exhibit distinct symmetry from the band structure of regular lattices. The theoretical model provides a way to further understand the physical mechanism of an ACI in terms of acoustic waves, which demonstrates that the breaking of time-reversal symmetry in the ACI originates from the Doppler effect induced by the vortex flows. The theoretical framework also presents a method to achieve the Hamiltonian from fundamental acoustic wave equations and can also be applied in the research of other acoustic topological materials, which provides a universal way to reveal the mechanism of acoustic wave manipulation with topological materials.

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• Acoustics
• Topological materials
• Band structure methods
• Bloch wave theory