Discovering topological surface states of Dirac points in an acoustic crystal

Dirac materials, unlike the Weyl materials, have not been found in experiments to support intrinsic topological surface states, as the surface arcs in existing systems are unstable against symmetry-preserving perturbations. Utilizing the proposed glide and time-reversal symmetries, we theoretically design and experimentally verify an acoustic crystal of two frequency-isolated three-dimensional Dirac points with Z₂ monopole charges and four gapless helicoid surface sheets. Under symmetry breakings, the 3D ideal Dirac point breaks into Z₂ Weyl dipoles, Z₂ nodal rings or a full bandgap.