Defective Edge states and Anomalous Bulk-boundary Correspondence for Topological Insulators under Non-Hermitian Similarity Transformation

Abstract

It was known that for non-Hermitian topological systems due to the non-Hermitian skin effect, the bulk-edge correspondence is broken down. In this paper, by using one-dimensional Su-SchriefferHeeger model and two-dimensional (deformed) Qi-Wu-Zhang model as examples, we focus on a special type of non-Hermitian topological system without non-Hermitian skin effect-topological systems under non-Hermitian similarity transformation. In these non-Hermitian systems, the defective edge states and the breakdown of bulk-edge correspondence are discovered. To characterize the topological properties, we introduce a new type of inversion symmetry-protected topological invariant-total Z2 topological invariant. In topological phases, defective edge states appear. With the help of the effective edge Hamiltonian, we find that the defective edge states are protected by (generalized) chiral symmetry and thus the (singular) defective edge states are unstable against the perturbation breaking the chiral symmetry. In addition, the results are generalized to nonHermitian topological insulators with inversion symmetry in higher dimensions. This work could help people to understand the defective edge states and the breakdown of bulk-edge correspondence for non-Hermitian topological systems.

arXiv comment13pages,8figures

References in corpus (57)

• Topological Insulators
• Topological insulators and superconductors
• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• Edge states and topological invariants of non-Hermitian systems
• Colloquium: Topological Band Theory
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Band Theory for Non-Hermitian Hamiltonians
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Non-Hermitian Chern bands
• Anatomy of skin modes and topology in non-Hermitian systems
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Edge states and topological phases in non-Hermitian systems
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Topological phase transition in non-Hermitian quasicrystals
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Topologically protected midgap states in complex photonic lattices
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Higher-order topological corner states induced by gain and loss
• Topological states of non-Hermitian systems
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Majorana bound states from exceptional points in non-topological superconductors
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Topological invariance and global Berry phase in non-Hermitian systems
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Anomalous helical edge states in a non-Hermitian Chern insulator
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Parity-time-symmetric topological superconductor
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Non-Hermitian topology: a unifying framework for the Andreev versus Majorana states controversy
• Knotted Non-Hermitian Metals
• Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
• Topological classification of non-Hermitian systems with reflection symmetry
• Topological quantum wires with balanced gain and loss
• Boundary Fidelity and Entanglement in the symmetry protected topological phase of the SSH model
• Time-Reversal Symmetry in Non-Hermitian Systems
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• Finite-size effects in non-Hermitian topological systems
• Symmetry protected topological phases characterized by isolated exceptional points
• Topological Phase Transition Independent of System Non-Hermiticity
• Topology and exceptional points of massive Dirac models with generic non-Hermitian perturbations
• Inversion symmetric non-Hermitian Chern insulator
• Non-Hermitian Hamiltonians and similarity transformations

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