Atomic Design of Three-Dimensional Photonic $Z_2$ Dirac and Weyl Points

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Abstract

Topological nodal points such as Dirac and Weyl points in photonic spectrum, as monopoles of the synthetic gauge fields in ${\vec k}$-space, offer unique abilities of manipulating light. However, designing topological nodal points in photonic crystals is much more difficult than in electronic band materials due to lack of the atomic picture. Here we propose an atomic approach for the design of three-dimensional Dirac and Weyl points via Mie resonances which can be regarded as photonic local orbits, using hollow-cylinder hexagonal photonic crystal as an example. We discover a new type of topological degeneracy, the $Z_2$ Dirac points, which are monopoles of the $SU(2)$ Berry-flux. Our study provides effective methodology as well as a new prototype of topological nodal points for future topological photonics and applications.