Experimental observation of Weyl points

In 1929, Hermann Weyl derived [1] the massless solutions from the Dirac equation – the relativistic wave equation for electrons. Neutrinos were thought, for decades, to be Weyl fermions until the discovery of the neutrino mass. Moreover, it has been suggested that low energy excitations in condensed matter[2–8] can be the solutions to the Weyl Hamiltonian. Recently, photons have also been proposed to emerge as Weyl particles inside photonic crystals [9]. In all cases, two linear dispersion bands in the three-dimensional (3D) momentum space intersect at a single degenerate point – the Weyl point. Remarkably, these Weyl points are monopoles of Berry flux with topological charges defined by the Chern numbers[2, 3]. These topological invariants enable materials containing Weyl points to exhibit a wide variety of novel phenomena including surface Fermi arcs[10], chiral anomaly[11], negative magnetoresistance[12], nonlocal transport[13], quantum anomalous Hall effect[14], unconventional superconductivity[15] and others [16, 17]. Nevertheless, Weyl points are yet to be experimentally observed in nature. In this work, we report on precisely such an observation in an inversion-breaking 3D double-gyroid photonic crystal without breaking time-reversal symmetry. Weyl points are sources of quantized Berry flux of ±2π in the momentum space. Their charges can be defined by the corresponding Chern numbers of ±1, as shown in Fig. 1a. So, Weyl points robustly appear in pairs and can only be removed through pair annihilation. Since the Berry curvature is strictly zero under PT symmetry, — the product of parity (P, inversion) and time-reversal symmetry (T ), isolated Weyl points only exist when at least one of P or T is broken. In Ref. [9], frequency-isolated Weyl points were predicted in PT -breaking DG photonic crystals. We chose to break P instead of T , in the experiment, to avoid using magnetic materials and applying static magnetic fields. This also allows our approach to be directly extended to photonic crystals at optical wavelengths. This P-breaking DG is shown in its bodycentered-cubic (bcc) unit cell in Fig. 1b. At the presence of T , there must exist even pairs of Weyl points. The two pairs of Weyl points illustrated in the Brillouin zone (BZ), in Fig. 1c, are thus the minimum number of Weyl points possible. The bandstructure plotted in Fig. 1d shows two linear bandcrossings along Γ − N and Γ − H. The other two Weyl points have identical dispersions due to T . We work at the microwave frequencies around 10GHz for the accessible fabrication of 3D photonic crystal. The current