Topological edge states on the acoustic Mobius band

Mobius molecules, such as Mobius annulenes and cyclacenes, are commonly existed in nature, which are usually classified and assembled by different twist numbers, and display discrepant Mobius topology and rich configurations. However, the Mobius geometries in acoustic crystals have rarely been investigated, as well as their topological effects. Here, we propose acoustic lattices on Mobius band with different configurations, where the topological edge states propagating in three-dimensional (3D) trajectories are clearly observed. These Mobius geometries can exhibit one or two integrated channels and display great robustness for guiding sound waves. The mapping between Mobius topology and lattice symmetries are also given for studying the in-gapped edge states by band dispersions. Our results provide a route to flexibly mimic the Mobius molecules by curved lattices and may inspire further research on, e.g., topological phenomena for classical waves in Mobius or other curved geometries.