Experimental Observation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math>-Dependent Bulk-Edge Correspondence in Sonic Semimetals with High Winding Numbers

The bulk-edge correspondence plays a crucial role in topological physics bridging the gap between the bulk topology and the topological edge states, which recently was extended to topological metamaterials having a large number of topological boundary states. In this work, we experimentally observe the k-dependent bulk-edge correspondence in the framework of a manmade sonic semimetal, supporting the coexistence of multiple topological phases which are separated by boundaries formed by versatile types of Dirac points. The structure is composed of stacked one-dimensional (1D) extended Su-Schrieffer-Heeger chains through long-range couplings, in which the topological phases are characterized by k-dependent winding numbers. Through an elaborately designed methodology for measuring the acoustic pressure amplitude and phase, we not only derive k-dependent topological winding numbers but also clearly observe the spatial distribution characteristics of edge states across different phases. Our findings significantly broaden the understanding of these critical topological phases and open up avenues for the manipulation of classical waves.