Acoustic Multiplexing Based on Higher-Order Topological Insulators with Combined Valley and Layer Degrees of Freedom

Higher-order topological insulators (HOTIs) in classical systems, featuring robust multidimensional boundary states protected by various crystalline symmetries, have become a fast-growing research branch in the vast topological family. Therein, valley pseudospins and layer pseudospins are separately introduced as extra degrees of freedom (DOFs) to manipulate topological phases. Here, we experimentally demon-strate that, by combining valley and layer DOFs, intriguing HOTIs can be realized. They host topological edge and corner states that are simultaneously valley dependent and layer polarized. We implement such HOTIs in bilayer sonic crystals (SCs) consisting of carefully stacked triangular scatterers. By rotating the scatterers, the valley and layer DOFs are interplayed, producing combined valley-layer polarizations. Correspondingly, the SCs exhibit versatile sound transport and localization. This inspires us to design an acoustic multiplexer, where sound waves can be guided along specific directions or trapped at specific locations, depending on the excitation frequencies. Our study of higher-order topology based on the inter-play between valley and layer DOFs enriches the topological physics. With combined valley and layer polarizations, the resultant HOTIs also offer versatile ways to guide and/or trap sound waves, which have potential applications in integrated and multiplexing phononic devices.