We discover experimentally second-order topological insulating phases and multidimensional topological transitions (in both bulk and edges) in sonic crystals. The higher-order topology and multidimensional transitions are triggered by tuning the geometry of the unit-cells of the sonic crystals.

Nature Physics 15, 582-588 (2019)

Link to the paper: https://www.nature.com/articles/s41567-019-0472-1