Figure 1: Realization of Weyl points in an electromagnetic system by introducing interlayer coupling.

(a) Unit cell of a single-layer system built from a hexagonal array of perfect electric conductor (PEC) cylinders bounded by two PEC slabs. This can be realized with metal-coated PCBs that are pierced through by a hexagonal array of aluminium rods. PCBs stacked in the z direction form a 3D photonic crystal. (b) Multilayer system built from PCBs stacked in the z direction. Interlayer couplings are introduced by the Y-shaped slots on two sides of the PCBs. (c) Top view of the unit cell (dashed hexagon) of the multilayer system. Blue and red areas highlight the Y-shaped slots on the upper surface and the lower surface of the PCBs. (d) Reciprocal space of a hexagonal lattice. Since the photonic crystal has translational symmetry along the z direction, k_z is a good quantum number. The system with a fixed k_z has a 2D band structure in the reduced Brillouin zone (grey plane in d). Chern numbers are well defined for each k_z slice. Weyl points can be viewed as the phase transition points between the k_z slices with different Chern numbers. (e) Bulk band structure in the k_z=0 plane. The structure has several Weyl points with different charges (in different colours). (f) Bulk band structure in the k_z=0.05π/d plane. (g–i). Dispersion along the z direction at , and , respectively. Bands with different rotational eigenvalues are plotted in different colours. Since a change in rotational eigenvalue results in a change in the band (gap) Chern number, each crossing point in g or h is a Weyl point whose charge depends on the ratio between the rotational eigenvalues of two intersecting bands. Four Weyl points between the 4th and 5th bands, which induce the jumps in the Chern number of the 5th band in j, are highlighted in g. (j) Chern numbers of the 5th gap (red solid line) and the 5th band (black dashed line) as a function of k_z, the jump in which implies the topological charge of associated Weyl points.