The on-site potentials may break the symmetry of a system, resulting in the loss of its original topology protected by the symmetry. In this work, we study the counteracting effect of non-Hermitian terms on real potentials, resulting in dynamically stable topological edge states. We show exactly for a class of systems that the spectrum remains unchanged in the presence of balanced perturbations. As a demonstration, we investigate an extended non-Hermitian Su-Schrieffer-Heeger (SSH) ladder. We find that the bulk-boundary correspondence still holds, and the zero-energy edge states become coalescing states. In comparison to the original SSH chain, such edge states are robust not only against local perturbations but also in the time domain. As a result, a trivial initial state can always evolve to a stable edge state. Our results provide insights for the application of time-domain stable topological quantum devices.

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• Edge states
• Topological phases of matter
• Exceptional points
• Non-Hermitian systems
• Lattice models in condensed matter
• Numerical techniques
• Tight-binding model