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

TL;DR

This paper explains the robustness of $ ext{Z}_2$ topological phases in stacked Hermitian systems by linking it to level repulsion in associated non-Hermitian systems, providing a systematic understanding of their stability.

Contribution

It offers a systematic explanation for the stability of $ ext{Z}_2$ topological phases in Hermitian systems through non-Hermitian level repulsion mechanisms.

Findings

Robust $ ext{Z}_2$ phases originate from non-Hermitian level repulsion.

Demonstrates stability in class DIII superconductors with $ ext{Z}_2$ topology.

Connects Hermitian topological stability to non-Hermitian topology.

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.