The coupling between valley and layer degrees of freedom provides a powerful route to extend higher-order topological boundary states. Here, we comprehensively investigate the higher-order corner states in two-dimensional bilayer triangular-lattice sonic crystals, arising from the combined effects of valley physics and bilayer topology. By independently rotating the scatterers in each layer, four distinct bulk topological phases are realized, characterized by different Wannier-center configurations and opposite fractional polarizations. Their pairwise combinations give rise to a wide variety of experimentally observed corner states, including layer-mixed, layer-polarized, and layer-locked modes. Moreover, valley-selective geometrical designs further modulate the spatial localization and operating frequencies of these corner states. Our results establish a versatile platform for manipulating topological acoustic states and open avenues for applications such as acoustic multiplexing, selective signal routing, and localized energy harvesting.

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• Mechanical & acoustical properties
• Symmetry protected topological states
• Topological insulators
• Topological phase transition
• Topological phases of matter