Symmetry-enforced three-dimensional Dirac phononic crystals

Dirac semimetals,the materials featuring fourfold degenerate Dirac points,are critical states of topologically distinct phases.Such gapless topological states have been accomplished by a band-inversion mechanism,in which the Dirac points can be annihilated pairwise by perturbations without changing the symmetry of the system.Here,we report an experimental observation of Dirac points that are enforced completely by the crystal symmetry using a nonsymmorphic three-dimensional phononic crystal.Intriguingly,our Dirac phononic crystal hosts four spiral topological surface states,in which the surface states of opposite helicities intersect gaplessly along certain momentum lines,as confirmed by additional surface measurements.The novel Dirac system may release new opportunities for studying elusive(pseudo)and offer a unique prototype platform for acoustic applications.