Flexible dimensional hierarchy of higher-order topology in the stacked Kagome-chain acoustic crystal

Abstract Manipulating wave propagation and energy collection plays a core role in modern physics, for which topological insulators hosting robust boundary states offer an ideal platform. However, there exist challenges integrating multiple like two-dimensional (2D) surface state, one-dimensional (1D) hinge zero-dimensional (0D) corner state into single three-dimensional (3D) architecture. Here we introduce dimensional hierarchy acoustic structure with piled 3D Kagome-chain crystal. By tuning the inter- intra-layer hopping, lift bulk 2D states. A further distortion on in-plane unit cell makes system support 1D 0D simultaneously. This keeps parent architecture unchanged. Analytically, prove robustness of our framework different geometrical configurations. Our research offers insight practical use sonic or optical device diversified modes concentrations transmissions.