Demonstration of non-Abelian frame charge flow in photonic crystals

Abstract: In PT symmetric systems, the notion of non-Abelian frame charges enables multiband topological characterization of the degeneracy nodes through examining the eigenvector frame rotations. Interestingly, some features of these frame charges can be viewed as an analogue of electric charges confined in conducting wires, only that they flow in momentum space along nodal lines. However, these frame charges are not integers, and non-Abelian signatures emerge when braiding between adjacent band nodal lines occurs, which flips the direction of the flow. In photonic systems, we discover that the photonic {\Gamma} point serves as the source or sink of such frame charge flow due to a hidden braiding induced by the often-ignored electrostatic mode at zero-frequency. We use biaxial photonic crystals as examples and show how complex nodal line configurations can be explained as the topological consequences of the frame charge flow from the {\Gamma} point to the Brillouin zone boundaries. We further designed and fabricated meta-crystals to experimentally observe these line nodes as manifestation of the non-Abelian frame charge flow.