Observation of topological switch between Weyl semimetal and third-order topological insulator phases

Weyl semimetals and higher-order topological insulators represent two fundamental yet distinct classes of topological matter. While both have been extensively studied in classical-wave systems, their coexistence and controllable transition within a single platform remain largely unexplored. Meanwhile, implementing three-dimensional spin-orbit couplings, which is crucial for realizing a broad class of higher-dimensional topological phases, continues to pose significant experimental challenges. Here, we experimentally realize three-dimensional spin-orbit couplings and demonstrate that tuning the dimerized spin-orbit coupling strength enables both the coexistence of and a controllable switch between Weyl semimetal and third-order topological insulator phases. By engineering a three-dimensional circuit metamaterial, we synthesize the required spin-orbit interactions and observe hallmark signatures of both phases: frequency spectroscopy reveals the Fermi arcs, while local density of states measurements identify the topological corner modes. Interestingly, the corner mode degeneracy doubles compared to that in the canonical Benalcazar-Bernevig-Hughes model, signaling an enriched topological structure. Our study establishes a fundamental connection between two paradigmatic topological phases and paves the way for further exploring spin-orbit-coupling induced exotic higher-dimensional topological phases.