Observation of multi-type corner states in right-angled trapezoidal sonic crystals

Abstract

Previous research has demonstrated corner states with various angular types through distinct structural configurations. However, achieving multiple corner state types within a single lattice has remained elusive. This study addresses the challenge in realizing multi-type corner states within a unified lattice design by introducing a novel right-angled trapezoidal topological sonic crystal. We propose a two-dimensional C-shaped square-lattice unit cell with $p4gg$ symmetry, which facilitates the realization of topological quadrupoles without relying on tight-binding mechanisms. The topological properties within the quadrupole topological band gap are confirmed through Wannier band and nested Wannier band calculations, with the location of Wannier centers accurately predicting the distribution of edge and corner states. To illustrate this, we construct both square-shaped and right-angled trapezoidal sonic crystals with a unified lattice design. Unlike the square-shaped structure, the trapezoidal design supports multi-type corner states at distinct frequencies, accommodating obtuse, right, and acute angles. An additional in-gap hypotenuse edge state underscores the versatility of this design. Experimental results validate these theoretical predictions, offering concrete evidence of multi-type corner states and their unique behaviors. This innovative approach not only simplifies the realization of topological quadrupoles but also opens new avenues for applications in acoustic wave control, energy harvesting, and precise sound manipulation.