Observation of two-dimensional time-reversal broken non-Abelian topological states.

Going beyond the conventional theory, non-Abelian band topology reveals the global quantum geometry of multiple Bloch bands and unveils a new paradigm for topological physics. However, to date, experimental studies on non-Abelian topological states beyond one dimension are still restricted to systems with time-reversal ( ) symmetry. Here, exploiting a designer gyromagnetic photonic crystal, we find rich -broken non-Abelian topological phases and their transitions with an unexpected connection to multigap antichiral edge states. By in-situ tuning the magnetic field in the gyromagnetic photonic crystal, we can create, braid, merge, and split the non-Abelian topological nodes in a unique way. Alongside this process, the multigap antichiral edge states can be tuned versatilely, giving rise to topological edge waveguiding with frequency-dependent directionality. These findings open a new avenue for non-Abelian topological physics and topological photonics.