Observation of fourfold nodal hinges and toruslike surface modes in acoustic metamaterials

Three-dimensional topological semimetals have attracted tremendous attention across multiple disciplines. Recently, a novel class of nodal-line semimetals hosting fourfold nodal hinges has been proposed, which manifests as four-band degeneracies pinning at the hinges of the three-dimensional Brillouin zone. Markedly different from the conventional nodal line featuring a nontrivial $\ensuremath{\pi}$ Berry phase that brings about drumhead surface modes, the fourfold nodal hinge carries a Berry phase of $2\ensuremath{\pi}$ and yields exotic toruslike surface modes. However, this fascinating nodal-line semimetal phase has not yet been reached experimentally. Here, we report a concrete construction of acoustic metamaterials with such symmetry-enforced fourfold nodal hinges and present convincing experimental evidence for the highly desired topological objects and the consequent toruslike surface modes. In addition, we also identify the twofold nodal walls and hourglass nodal lines in this system, where the latter feature drumhead surface states as usual. Our study may offer new possibilities for manipulating acoustic surface waves and exploring unique topological semimetal phases.