Antihelical edge states in two-dimensional photonic topological metals

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Topological edge states are the core of topological photonics. Here we introduce the antihelical edge states of time-reversal symmetric topological metals and propose a photonic realization in an anisotropic square lattice of coupled ring resonators, where the clockwise and counterclockwise modes play the role of pseudospins. The antihelical edge states robustly propagate across the corners toward the diagonal of the square lattice: The same (opposite) pseudospins copropagate in the same (opposite) direction on the parallel lattice boundaries; the different pseudospins separate and converge at the opposite corners. The antihelical edge states in the topological metallic phase alter to the helical edge states in the topological insulating phase under a metal-insulator phase transition. The antihelical edge states provide a unique manner of topologically-protected robust light transport applicable for topological purification. Our findings create new opportunities for topological photonics and metamaterials.