Three-dimensional photonic crystal with Z2 Dirac and Weyl points

As monopoles of the synthetic gauge fields in k-space, topological nodal points such as Dirac and Weyl points in photonic spectrum offer unique abilities of manipulating light, such as achieving zero refractive index, Klein tunneling, and single-mode lasing enhancement. It is also found that 3D Weyl points can provide effective angle and frequency selective transmission. However, designing topological nodal points in photonic crystals is much more difficult than in electronic band materials. Here we propose an atomic picture for designing three-dimensional Dirac and Weyl points via Mie resonances, which could be regarded as photonic local orbits. By using hollow-cylinder hexagonal photonic crystal as an example (in hexagonal lattice with C
6v
symmetry, only the L
z
= 0, 1, 2, 3 orbits are distinguishable and thus can be viewed as s, p, d, f orbits), we discover a pair of stable topological Z
2
Dirac points as monopoles of the SU(2) Berry flux. Furthermore, we introduce an inversion symmetry breaking mechanism by twisting the unit cells and find that each Dirac point splits into a pair of Weyl points with opposite chirality. We also present the phase diagrams of Dirac and Weyl points to show their robustness. Our study provides effective methodology as well as prototype of topological nodal points for future topological photonics and applications.