Origin of Robust $\mathbb{Z}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion

• URL: http://arxiv.org/abs/2407.20759v3
• Date: Wed, 04 Dec 2024 08:25:40 GMT
• Title: Origin of Robust $\mathbb{Z}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion
• Authors: Zhiyu Jiang, Masatoshi Sato, Hideaki Obuse,
• Abstract summary: Quantum spin Hall insulators, which possess a non-trivial $mathbbZ$ topological phase, have attracted great attention for two decades.<n>It is generally believed that when an even number of layers of the quantum spin Hall insulators are stacked, the $mathbbZ$ topological phase becomes unstable due to $mathbbZ$ nature.<n>We provide a systematic understanding that the robustness generally originates from level repulsion in the corresponding non-Hermitian system derived from Hermitization.
• Score: 0.8739101659113157
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Quantum spin Hall insulators, which possess a non-trivial $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ topological phase becomes unstable due to $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ topology and the corresponding non-Hermitian 1D system in class AII$^\dagger$ with $\mathbb{Z}_2$ point-gap topology.

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