Non-Hermitian Topology in Hermitian Topological Matter

Abstract

Non-Hermiticity gives rise to distinctive topological phenomena absent in Hermitian systems. However, connection between such intrinsic non-Hermitian topology and Hermitian topology has remained largely elusive. Here, considering the bulk and boundary as an environment and system, respectively, we demonstrate that anomalous boundary states in Hermitian topological insulators exhibit non-Hermitian topology. We study the self-energy capturing the particle exchange between the bulk and boundary, and show that it detects Hermitian topology in the bulk and induces non-Hermitian topology at the boundary. As an illustrative example, we reveal non-Hermitian topology and concomitant skin effect inherently embedded within chiral edge states of Chern insulators. We also identify the emergence of hinge states within effective non-Hermitian Hamiltonians at surfaces of three-dimensional topological insulators. Furthermore, we comprehensively classify our correspondence across all the tenfold symmetry classes of topological insulators and superconductors. Our work uncovers hidden connection between Hermitian and non-Hermitian topology, and provides an approach to identifying non-Hermitian topology in quantum matter.

arXiv comment9+10 pages, 5+1 figures

References in corpus (107)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Edge states and topological invariants of non-Hermitian systems
• Periodic table for topological insulators and superconductors
• Exceptional Topology of Non-Hermitian Systems
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Lasing in topological edge states of a 1D lattice
• Non-Hermitian Chern bands
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Non-Hermitian Boundary Modes
• Topological phases of fermions in one dimension
• Spawning rings of exceptional points out of Dirac cones
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• The effects of interactions on the topological classification of free fermion systems
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Edge states and topological phases in non-Hermitian systems
• Non-reciprocal robotic metamaterials
• 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
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Universal non-Hermitian skin effect in two and higher dimensions
• Topological Hybrid Silicon Microlasers
• Reciprocal skin effect and its realization in a topolectrical circuit
• Topologically protected midgap states in complex photonic lattices
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Non-Hermitian topological phenomena: A review
• Higher-order non-Hermitian skin effect
• Experimental realization of a Weyl exceptional ring
• Observation of higher-order non-Hermitian skin effect
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Robust light transport in non-Hermitian photonic lattices
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
• Tunable non-reciprocal quantum transport through a dissipative Aharonov-Bohm ring in ultracold atoms
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Tenfold Way for Quadratic Lindbladians
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Second-order topological non-Hermitian skin effects
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Topological framework for directional amplification in driven-dissipative cavity arrays
• Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
• Perspective on topological states of non-Hermitian lattices
• Nodal Arc in Disordered Dirac Fermions: Connection to Non-Hermitian Band Theory
• Non-Hermitian second-order skin and topological modes
• Non-Hermitian Weyl Physics in Topological Insulator Ferromagnet Junctions
• Bulk-boundary correspondence for non-Hermitian Hamiltonians via Green functions
• Hybrid skin-topological modes without asymmetric couplings
• Guided accumulation of active particles by topological design of a second-order skin effect
• Exceptional Topological Insulators
• Topological Field Theory of Non-Hermitian Systems
• Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems
• Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
• Boundary Fidelity and Entanglement in the symmetry protected topological phase of the SSH model
• Non-Hermitian Skin Effects in Hermitian Correlated/Disordered Systems: Boundary-Sensitive/Insensitive Quantities and Pseudo Quantum Number
• Non-Hermitian topology of spontaneous magnon decay
• Time-Reversal Symmetry in Non-Hermitian Systems
• Equivalence of the effective non-hermitian Hamiltonians in the context of open quantum systems and strongly-correlated electron systems
• Non-Hermitian physics without gain or loss: the skin effect of reflected waves
• Green function techniques in the treatment of quantum transport at the molecular scale
• Topology and Observables of the Non-Hermitian Chern Insulator
• Non-Hermitian Chiral Skin Effect
• Hermitian Bulk -- Non-Hermitian Boundary Correspondence
• Photonic corner skin modes
• Zoology of non-Hermitian spectra and their graph topology
• Observation of non-Hermitian topology in a multi-terminal quantum Hall device
• Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects
• Bulk-boundary correspondence in point-gap topological phases
• Universal platform of point-gap topological phases from topological materials
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Non-Hermitian boundary spectral winding
• Topological enhancement of non-normality in non-Hermitian skin effects
• Non-Hermitian phase-biased Josephson junctions
• Emergent non-Hermitian models
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Dynamically Induced Exceptional Phases in Quenched Interacting Semimetals
• What is the resonant state in open quantum systems?

Cited by in corpus (10)

• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• $K$-theory classification of Wannier localizability and detachable topological boundary states
• Exceptional second-order topological insulators
• Gauge Field Induced Unconventional Skin Effect in Spinful Non-Hermitian Systems
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Non-Hermitian Hopf insulators
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Phase transition from Weyl to self-linked semimetal using bi-circular laser
• Emergence of Hermitian topology from non-Hermitian knots