Abstract
Quantum spin Hall insulators, which possess a non-trivial Z₂ topological phase, have attracted great attention for two decades. It is generally believed that when an even number of layers of the quantum spin Hall insulators are stacked, the Z₂ topological phase becomes unstable due to Z₂ nature. While the counterexamples of the instability were observed in several literates, there is no systematic understanding. In this work, we provide a systematic understanding that the robust Z₂ topological phase in a Hermitian system with chiral symmetry against stacking. We clarify that the robustness generally originates from level repulsion in the corresponding non-Hermitian system derived from Hermitization. We demonstrate this by treating a class DIII superconductor in 1D with Z₂ topology and the corresponding non-Hermitian 1D system in class AII^† with Z₂ point-gap topology.