Non-Abelian Frame Charge Flow in Photonic Media

In PT -symmetric systems, the notion of non-Abelian frame charges enables multiband topological characterization of degeneracies by examining the eigenvector-frame rotations. Interestingly, some features of these frame charges can be viewed as an analog of electric charges confined in conducting wires, only that they flow in momentum space along nodal lines. But different from electric charges, 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, the photonic Γpoint serves as the source or sink of such a frame charge flow due to a hidden braiding induced by the often-ignored electrostatic mode at zero frequency. This source naturally generates non-Abelian topological signatures in PT -symmetric photonic systems that can be identified even in ordinary dielectric media. We use biaxial photonic crystals as examples to show how complex nodal line configurations can be explained as the topological consequences of the frame charge flow from the Γ point to the Brillouin zone boundaries. Our results reveal that non-Abelian band topology is intrinsically manifested in general photonic systems, making them easily accessible platforms for exploring non-Abelian physics.