Spin-Chern insulator induced by pseudospin-orbit coupling in phononic crystals

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The boundary modes of classical waves protected by the topology are of great significance for robust energy transmission and reliable information processing. Many endeavors have been made to realize topological insulators in electromagnetic, mechanical and acoustic systems. Previous studies on acoustic boundary modes mainly focused on the interface states at the domain walls between different topological phases of phononic crystals. In electromagnetic and mechanical systems, although helical boundary states have been observed, the pseudospin in them is conserved, thus these systems can be considered as two independent copies of Chern insulators. When the pseudospin conservation is broken, the topology cannot be described by Chern numbers, and the spin will vary in transport. This general case remains to be explored both in electronic and classical systems. In this work, we constructed a two-dimensional topological phononic crystal induced by pseudospin-orbit coupling, which hosts the gapless helical boundary modes at the edge of a phononic crystal. Since these boundary states originate from non-zero spin-Chern numbers, the system is called the spin-Chern insulator. We have observed these boundary states in experiments, and observed the spin-flipping transport in the H-shaped sample, proving the spin non-conservation of the boundary states. Different from the earlier work, this work demonstrates two important aspects: first, the acoustic topological insulator is induced by the pseudospin-orbit coupling, and possesses the gapless helical edge states on its boundary, thus is the first analogue of topological insulator for acoustic wave; second, the inherent spin conservation is broken, which expands and deepens the knowledge of current topological physics in classical and electronic systems. The helical boundary states may have potential applications in new topological acoustic devices.