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

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${}^{†}$ with ${\mathbb{Z}}_2$ point-gap topology.

arXiv comment13 pages, 11 figures

References in corpus (64)

• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Unpaired Majorana fermions in quantum wires
• Topological Insulators in Three Dimensions
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Edge states and topological invariants of non-Hermitian systems
• Quantum Spin Hall Effect
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• PT-Symmetric Quantum Mechanics
• Symmetry and Topology in Non-Hermitian Physics
• Large-gap quantum spin Hall insulators in tin films
• Topological Origin of Non-Hermitian Skin Effects
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Non-Bloch Band Theory of Non-Hermitian Systems
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Edge states and topological phases in non-Hermitian systems
• Universal non-Hermitian skin effect in two and higher dimensions
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Non-Hermitian topological phenomena: A review
• Higher-order non-Hermitian skin effect
• New topological invariants in non-Hermitian systems
• Non-Hermitian Delocalization and Eigenfunctions
• Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• The strong side of weak topological insulators
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Stacked topological insulator built from bismuth-based graphene sheet analogues
• Non-Hermitean Random Matrix Theory: method of hermitization
• High-order exceptional points in optomechanics
• Majorana Kramers Doublets in $d_{x^2-y^2}$-wave Superconductors with Rashba Spin-Orbit Coupling
• Quantum Spin Hall Insulators with Interactions and Lattice Anisotropy
• Non-Hermitian Dirac Cones
• Disordered weak and strong topological insulators
• Room-temperature quantum spin Hall edge state in a higher-order topological insulator Bi${}_4$Br${}_4$
• Inner Skin Effects on Non-Hermitian Topological Fractals
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• Non-Hermitian skin effect and self-acceleration
• Time-Reversal Symmetry in Non-Hermitian Systems
• Equivalent topological invariants for one-dimensional Majorana wires in symmetry class D
• Non-Hermitian Chiral Skin Effect
• Crossover from Majorana edge to end states in quasi-one-dimensional p-wave superconductors
• Topological invariant for generic 1D time reversal symmetric superconductors in class DIII
• Many-body non-Hermitian skin effect under dynamic gauge coupling
• DIII Topological Superconductivity with Emergent Time-Reversal Symmetry
• Towards Layer-Selective Quantum Spin Hall Channels in Weak Topological Insulator Bi4Br2I2
• Dimensional crossover of transport characteristics in topological insulator nanofilms
• Comparative study of Weyl semimetal, topological and Chern insulators: thin-film point of view
• Topological crystalline insulators from stacked graphene layers
• Bulk-edge correspondence and stability of multiple edge states of a $\mathcal{P}\mathcal{T}$ symmetric non-Hermitian system by using non-unitary quantum walks
• Photon and phonon statistics in a qubit-plasmon-phonon ultrastrong coupling system
• Bulk-Edge Correspondence for Point-Gap Topological Phases in Junction Systems
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk