Double Gyroids for Frequency-Isolated Weyl Points in the Visible Regime and Interference Lithographic Design

Easy-to-craft photonic crystals enabling frequency-isolated Weyl points, especially at visible wavelengths, are yet to be developed. To this end, we exploited double gyroid (DG) crystals with Parity (P)-breaking and nanoscale unit cells, which are readily compatible with currently accessible interference lithography (IL). By modulating a level-set equation, we designed the D₂-symmetric single gyroid (SG), perturbed from an O-symmetric SG, and found that the DG crystals, consisting of D₂- and O-symmetric SGs with opposite chirality, can exhibit frequency-isolated Weyl points. As a route to the fabrication of the designed P-breaking DG crystals with a nanoscale unit cell, the IL condition was defined in terms of (i) wavenumbers of multiple beams and (ii) their own complex electric fields. Our lithographically designed nanoscale DG crystals, even with a practical material condition, exhibited the Weyl points whose wavelengths were totally separated from other neighboring bands. Given the established design strategy suitable for a practical processing (e.g., IL), we have provided a viable route for on-chip integration of such Weyl materials, enabling topologically nontrivial surface states.