Recent studies have reported a puzzling phenomenon in non-Hermitian systems: topological zero eigenmodes (TZMs) appear and disappear as the system size varies, seemingly contradicting the inherent robustness of topology. This work demonstrates that these observations do not signify genuine topological phase transitions but instead stem from a transformation between “visible” and “hidden” zero eigenmodes. The latter are extremely long-lived excitations that are absent in the finite-system eigenspectrum yet exhibit nontrivial character and topological behavior distinct from the trivial phase. We show that the topological invariants—the winding numbers—precisely predict the number of protected zero singular values, which equals the total number of stable topological hidden and visible zero eigenmodes. We further demonstrate that two coupled nonreciprocal chains—such as coupled Su-Schrieffer-Heeger (SSH) models and nonreciprocal superconducting nanowires—provide a promising platform for detecting the hidden zero eigenmodes, differentiating them from the trivial phase, and unifying the bulk-boundary correspondence (BBC) for eigenvalues and singular values. The consistent behavior observed across these models establishes that size-induced TZMs originate from hidden zero eigenmodes, governed by a shared universal mechanism.

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• Anderson localization
• Skin effect
• Topological phase transition
• Non-Hermitian systems
• Su-Schrieffer-Heeger model
• Tight-binding model