Fig. 2: Acoustic realization of the double Dirac point and the three mass terms for the monopole design.

a The ideal Dirac acoustic crystal with the 8-band Dirac point in the super-cell. b, d, f The perturbed geometries defined by fD(r) + δfi(r), (i = x, y, z), whose band structures are plotted in (c) and (e). The rainbow-colored arrows represent the hedgehog form of the Dirac mass vector (mx, my, mz).