Three-dimensional Dirac semimetal metamaterial enabled by negative couplings

Three-dimensional (3D) semimetals with fourfold degenerate Dirac points are of prominent importance in topological photonics as the parent states to Weyl nodes, line nodes, & etc. The dispersions on all the momentums' directions are linear, which represents that the Dirac point and topologically protected helicoid surface states may exist. Here, we have demonstrated an acoustic metamaterial with Dirac points by designing the sign of coupling terms, specifically incorporating negative couplings. Tuning the coupling parameter along longitudinal direction, the transition from 3D Dirac point to Weyl points can be obtained. In realistic topological metamaterial designing, the negative coupling is realized by inserting additional off-resonant sites. The simulated band dispersion clearly shows four-band crossing point. The helicoid surface states are also proved. Our study provides a new approach of constructing 3D topological phase and shows the transition between nodal ring and Dirac point. Our results can be the theoretical basement of topological protected devices.