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Inspired by the discovery of quantum hall effect and topological insulator,topological properties of classical waves start to draw worldwide attention.Topological non-trivial bands characterized by non-zero Chern numbers arerealized with external magnetic field induced time reversal symmetry breakingor dynamic modulation. Due to the absence of Faraday-like effect, the breakingof time reversal symmetry in an acoustic system is commonly realized withmoving background fluids, and hence drastically increases the engineeringcomplexity. Here we show that we can realize effective inversion symmetrybreaking and effective gauge field in a reduced two-dimensional system bystructurally engineering interlayer couplings, achieving an acoustic analog ofthe topological Haldane model. We then find and demonstrate unidirectionalbackscattering immune edge states. We show that the synthetic gauge field isclosely related to the Weyl points in the three-dimensional band structure.

Synthetic gauge fields and Weyl point in Time-Reversal Invariant Acoustic Systems