Observation of a Charge-2 Photonic Weyl Point in the Infrared

Weyl points are robust point degeneracies in the band structure of a periodic material, which act as monopoles of Berry curvature. They have been at the forefront of research in three-dimensional topological materials as they are associated with novel behavior both in the bulk and on the surface. Here, we present the experimental observation of a charge-2 photonic Weyl point in a low-index-contrast photonic crystal fabricated by two-photon polymerization. The reflection spectrum obtained via Fourier-transform infrared spectroscopy closely matches simulations and shows two bands with quadratic dispersion around a point degeneracy.

Figure 1

Chiral woodpile PhC and corresponding band structure supporting a charge $+2$ Weyl point. (a) The chiral woodpile structure made by stacking layers of rods with an in-plane rotation of 45° between layers. (b) Band structure along $\mathbf{Y}-\mathbf{\Gamma }-\mathbf{X}$ showing bands 3 to 11. The Weyl point of interest is the degeneracy between bands 4 and 5 at $\mathbf{\Gamma }$ (blue circle). The 3D Brillouin zone of the PhC is shown in the inset. (c) Berry phase plot for band 4 around the $\mathbf{\Gamma }$ point. The double winding indicates that the degeneracy has a topological charge of 2.

Figure 2

Fabricated chiral woodpile PhC. FESEM image of a parity-breaking chiral woodpile fabricated using two-photon polymerization.

Figure 3

Observation of the charge $+2$ Weyl point in the reflection spectra of the chiral woodpile PhC. (a),(b),(c) Experimentally measured angle-resolved FTIR reflection spectra for 90° ($p$), 0° ($s$) and 45° polarizations, respectively. The dotted lines in all plots are Weyl bulk bands from MPB. (d),(e),(f) ${\mathrm{S}}^4$ (RCWA) simulation of the angle-resolved reflection spectra for all three polarizations.

Figure 4

Surface states associated with the Weyl point at $\mathbf{R}$ (a) The $k_z$-projected band structure for the truncated chiral woodpile PhC (${ϵ}_{\mathrm{rods}}=12$, rod $\text{width}=0.175a$, rod $\text{height}=0.25a$) along a loop enclosing the $\mathbf{M}$ point with radius 0.15 ($2\pi /a$) and parametric angle $0\le t/2\pi \le 1$. Solid colors are projections of bulk bands, the solid red and blue lines are surface states localized to the top and bottom surfaces, respectively, and the black dotted line marks the frequency of the Weyl point. (b)–(c) Magnetic field intensity of the surface state at $t/2\pi =0.25$ for ${ϵ}_{\mathrm{rods}}=12$ and 8, respectively. (d) Magnetic field intensity of the surface resonance for ${ϵ}_{\mathrm{rods}}=6$ calculated using FDTD method as implemented in MEEP [40].