Unveiling Real Triple Degeneracies in Crystals: Exploring Link and Compound Structures

With their non-Abelian topological charges, real multi-bandgap systems challenge the conventional topological phase classifications. As the minimal sector of multi-bandgap systems, real triple degeneracies (RTPs), which serves as real "Weyl points", lay the foundation for the research on real topological phases. However, experimental observation of RTP and physical systems with global band configuration consisting of multiple RTPs in crystals has not been reported. In this study, we employ Euler number to characterize RTPs, establish their connection with both Abelian and non-Abelian charges, and provide experimental evidence for the existence of RTPs in photonic meta-crystals. By considering RTPs as the basic elements, we further propose the concept of a topological compound, akin to a chemical compound, where we find that certain phases are not topologically allowed. The topological classification of RTPs in crystals demonstrated in our work plays a similar role as the "no-go" theorem in the Weyl system.