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

TL;DR

This paper reports the first experimental observation of real triple degeneracies in photonic meta-crystals, characterizing their topological properties and introducing the concept of topological compounds, advancing the understanding of real topological phases in crystals.

Contribution

It provides experimental evidence of RTPs in photonic crystals, characterizes their topological nature using Euler numbers, and introduces the concept of topological compounds.

Findings

Experimental demonstration of RTPs in photonic meta-crystals

Characterization of RTPs using Euler number and topological charges

Proposal of topological compounds and classification rules

Abstract

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 serve as real 'Weyl points', lay the foundation for the research on real topological phases. However, experimental demonstration of physical systems with global band configurations consisting of multiple RTPs in crystals has not been reported. Here we present experimental evidence of RTPs in photonic meta-crystals, characterizing them using the Euler number, and establishing their connection with both Abelian and non-Abelian charges. 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 Weyl systems.