Unconventional surface responses of fourfold-degenerate Dirac-nodal-line semimetals in sonic crystals

Three-dimensional nodal-line semimetals (NLSMs) are of remarkable importance for both enriching topological physics and wave management. However, NLSMs realized in acoustic systems are twofold band degenerate and are called Weyl NLSMs. Here, we report on the experimental observation of Dirac NLSMs with fourfold degeneracy in sonic crystals. We reveal that the topological properties of the Dirac NLSMs are entirely different than those of the conventional Weyl NLSMs. The Berry phase related to the Dirac nodal line (DNL) is $2\pi$, which results in surface responses of the Dirac NLSMs in two radically different situations: a torus surface state occupying the entire surface Brillouin zone (SBZ) and one without any surface state in the SBZ. We further reveal that topological surface arcs caused by the DNL can change from open to closed contours. The findings of Dirac NLSMs and their unique surface response may bring about exciting frontiers for the flexible manipulation of acoustic surface waves.