High-robust topological edge states in quasi-one-dimensional zigzag systems

Topological edge states in one-dimensional systems typically rely on symmetry protection, making them vulnerable to multiple types of disorder. Here, we demonstrate the emergence of remarkably resilient topologically protected edge states in a quasi-one-dimensional zigzag structure where some lattice couplings are negative. These states maintain their nature despite simultaneous disorders in lattice couplings, variations in on-site phases and potentials, and dissipation. Using a novel approach to restore bulk-boundary correspondence, we establish a continuous mapping between our model and a “parental model” with restored chiral symmetry, enabling computation of a regularized topological invariant. We propose practical implementations using orbital-induced synthetic flux in photonic waveguide arrays, showing good agreement between coupled mode theory and full-wave simulations. Our results reveal new mechanisms for achieving topological protection without conventional symmetries, with potential applications across multiple physical platforms including photonic, acoustic, and mechanical metamaterials.