Observation of Weyl point pair annihilation in a gyromagnetic photonic crystal

Abstract: Weyl semimetals are gapless three-dimensional (3D) phases whose bandstructures contain Weyl point (WP) degeneracies. WPs carry topological charge and can only be eliminated by mutual annihilation, a process that generates the various topologically distinct 3D insulators. Time reversal (T) symmetric Weyl phases, containing a minimum of four WPs, have been extensively studied in real materials, photonic metamaterials, and other systems. Weyl phases with a single WP pair - the simplest configuration of WPs - are more elusive as they require T-breaking. Here, we implement a microwave-scale gyromagnetic 3D photonic crystal, and use field-mapping experiments to track a single pair of ideal WPs whose momentum space locations depend strongly on the biasing magnetic field. By continuously varying the field strength, we observe the annihilation of the WPs, and the formation of a 3D Chern insulator, a previously unrealised member of the family of 3D topological insulators (TIs). Surface measurements show, in unprecedented detail, how the Fermi arc states connecting the WPs evolve into TI surface states.