Zak Phase and Gap Inversion in Periodic Acoustic Systems

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  Geometric phase is a useful concept in many physical systems.The Zak phase is a special kind of geometric phase that describes the topological property of an isolated band in one dimension system.In this talk,we will discuss the Zak phase of an acoustic system and its physical consequences.The Zak phase of an isolated band can assume two values only(either 0 or π)for a system with inversion symmetry,and the value of Zak phase is decided by the symmetry properties of band edge states.As the symmetry of the band edge states are also related to the reflection phase inside the band gap bounded by those band edge states,there exist a relationship between the reflection phase inside a band gap and the Zak phase of bulk Bloch bands.Thus by measuring the reflection phase at the boundary of a periodic acoustic system inside the band gap frequencies,we determine the Zak phases of bulk acoustic bands.We also find a topological transition point in a periodic acoustic band gap system where the Zak phases of bulk bands change.By turning the system parameters across this topological transition point,the analog of gap inversion in electronic topological insulators can be found in acoustic systems.The acoustic systems on different sides of this topological transition point are topologically different.When an interface is constructed between systems with different topological properties,an interface state will be formed at the boundary.We constructed such a system and verified the theoretical predictions experimentally.
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