Non-Hermitian Chern bands

Abstract

The relation between chiral edge modes and bulk Chern numbers of quantum Hall insulators is a paradigmatic example of bulk-boundary correspondence. We show that the chiral edge modes are not strictly tied to the Chern numbers defined by a non-Hermitian Bloch Hamiltonian. This breakdown of conventional bulk-boundary correspondence stems from the non-Bloch-wave behavior of eigenstates (non-Hermitian skin effect), which generates pronounced deviations of phase diagrams from the Bloch theory. We introduce non-Bloch Chern numbers that faithfully predict the numbers of chiral edge modes. The theory is backed up by the open-boundary energy spectra, dynamics, and phase diagram of representative lattice models. Our results highlight a unique feature of non-Hermitian bands and suggest a non-Bloch framework to characterize their topology.

arXiv comment11 pages, 12 figures, including supplemental material

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• Emerging exceptional point with breakdown of skin effect in non-Hermitian systems
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• Two-dimensional non-Hermitian topological phases induced by asymmetric hopping in a one-dimensional superlattice
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Polariton vortex Chern insulator
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• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
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• Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Skin Effect in Quadratic Lindbladian Systems: an Adjoint Fermion Approach
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• Observation of Impurity-Induced Scale-Free Localization in a Disordered Non-Hermitian Electrical Circuit
• Nontrivial worldline winding in non-Hermitian quantum systems
• Unravelling the edge spectra of non-Hermitian Chern insulators
• Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices
• Non-Bloch PT symmetry breaking: Universal threshold and dimensional surprise
• State-dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Topological quantum optical states in quasiperiodic cold atomic chains
• Constraints of internal symmetry on the non-Hermitian skin effect and bidirectional skin effect under the action of the Hermitian conjugate of time-reversal symmetry
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Selective and tunable excitation of topological non-Hermitian skin modes
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Investigation of a non-Hermitian edge burst with time-dependent perturbation theory
• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation
• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Non-Hermiticity stabilized Majorana zero modes in semiconductor-superconductor nanowires
• Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
• Hermitian chiral boundary states in non-Hermitian topological insulators
• Solvable dilation model of $\mathcal{P}\mathcal{T}$-symmetric systems
• Symmetry-Protected Topological Phase for Spin-Tensor-Momentum-Coupled Ultracold Atoms
• Transport effects in non-Hermitian nonreciprocal systems: General approach
• Equivalence and superposition of real and imaginary quasiperiodicities
• Discriminant indicators with generalized inversion symmetry
• Correlations in non-Hermitian systems and Diagram techniques for the steady state
• Information constraint in open quantum systems
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
• Complex semiclassical theory for non-Hermitian quantum systems
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Versatile Control of Nonlinear Topological States in Non-Hermitian Systems
• Biorthogonal topological charge pumping in non-Hermitian systems
• Non-Hermitian three-dimensional two-band Hopf insulator
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Non-Hermitian semi-Dirac semi-metals
• Tailoring Bound State Geometry in High-Dimensional Non-Hermitian Systems
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Anomalous pumping in the non-Hermitian Rice-Mele model
• Bulk-Edge Correspondence for Point-Gap Topological Phases in Junction Systems
• Edge states in a non-Hermitian topological crystalline insulator
• Eigenstate clustering around exceptional points
• Non-Hermitian skin effect in a single trapped ion
• Universal spectral moment theorem and its applications in non-Hermitian systems
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Interaction-Induced Second-Order Skin Effect
• Effective impurity behavior emergent from non-Hermitian proximity effect
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Non-Floquet engineering in periodically driven non-Hermitian systems
• Dynamics in non-Hermitian systems with nonreciprocal coupling
• Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• Practical quantum simulation of small-scale non-Hermitian dynamics
• Non-Hermitian superconducting diode effect
• General theory for infernal points in non-Hermitian systems
• Localization and topological transitions in generalized non-Hermitian SSH models
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• $\mathcal{P}\mathcal{T}$ symmetry of a square-wave modulated two-level system
• Wannier-Stark localization in one-dimensional amplitude-chirped lattices
• Universal hard-edge statistics of non-Hermitian random matrices
• Non-Bloch dynamics and topology in a classical non-equilibrium process
• Field Theoretical Study of Disorder in Non-Hermitian Topological Models
• Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media
• Entangelment Entropy on Generalized Brillouin Zone
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Fate of pseudo mobility-edge and multiple states in non-Hermitian Wannier-Stark lattice
• Chiral-Extended Photon-Emitter Dressed States in Non-Hermitian Topological Baths
• Excitation Transmission through a non-Hermitian traversable wormhole
• Defective Edge states and Anomalous Bulk-boundary Correspondence for Topological Insulators under Non-Hermitian Similarity Transformation
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Exceptional magic angles in non-Hermitian twisted bilayer graphene
• Symmetry classes of dissipative topological insulators with edge dark state
• Topological invariants of complex energy plane in non-Hermitian systems
• Dissipative two-dimensional Raman lattice
• Topological states at exceptional points
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Non-Bloch Dirac Points and Phase Diagram in the Stacked Non-Hermitian SSH Model
• Topological Singularities in Metasurface Scattering Matrices: From Nodal Lines to Exceptional Lines
• Quasi-stationary solutions in non-Hermitian systems
• The Quantum Skin Hall Effect
• Edge-selective extremal damping from topological heritage of dissipative Chern insulators
• Nonlinear Hall effects with an exceptional ring
• Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model
• Electronic polarization in non-Bloch band theory
• Inner non-Hermitian skin effect on Bethe lattice
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect
• Non-Hermitian $C_{NH}=2$ Chern insulator protected by generalized rotational symmetry
• Chiral Hinge Transport in Disordered Non-Hermitian Second-Order Topological Insulators
• Emergent non-Hermitian physics in generalized Lotka-Volterra model
• Spontaneous Formation of Exceptional Points at the Onset of Magnetism
• Correlations at higher-order exceptional points in non-Hermitian models
• Non-Quantized Edge Channel Conductance and Zero Conductance Fluctuation in Non-Hermitian Chern Insulators
• One-dimensional non-Hermitian band structures as Riemann surfaces
• Optical pumping through the Liouvillian skin effect
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Topological Phase Transition of A Non-Hermitian Crosslinked Chain
• Real-time edge dynamics of non-Hermitian lattices
• Many-body critical non-Hermitian skin effect
• Spin-dependent gain and loss in photonic quantum spin Hall systems
• Phase transitions as a manifestation of spontaneous unitarity violation
• Machine learning of mirror skin effects in the presence of disorder
• Composite Quantum Phases in Non-Hermitian Systems
• Discriminant indicator with generalized rotational symmetry
• Duality between Generalized Non-Hermitian HN Model in Flat Space and Hermitian System in Curved space
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Topological characteristics of gap closing points in nonlinear Weyl semimetals
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• Impurity in a Fermi gas under non-Hermitian spin-orbit coupling
• Ring-Frustrated Non-Hermitian $XY$ Model
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Tentaclelike spectra and bound states in Hatano-Nelson chain with long-range impurity coupling
• Antichiral and trap-skin dynamics in a nonreciprocal bosonic two-leg ladder with artificial magnetic flux
• Theory for the spectral splitting exponent of exceptional points
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• Optical non-Hermitian skin effect in two-dimensional uniform media
• Cutting off the non-Hermitian boundary from an anomalous Floquet topological insulator
• Winding Topology of Multifold Exceptional Points
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations
• Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions
• Exceptional second-order topological insulators
• Topology and its detection in a dissipative Aharonov-Bohm chain
• Controllable suppression of Non-Hermitian skin effects
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Quasiparticle picture of topological phase transitions induced by interactions
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Gauge Field Induced Unconventional Skin Effect in Spinful Non-Hermitian Systems
• Magnetization in a non-equilibrium quantum spin system
• Coalescing hardcore-boson condensate states with nonzero momentum
• Semi-localization transition driven by a single asymmetrical tunneling
• Topological extension including quantum jump
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Direct Measurement of a Non-Hermitian Topological Invariant in a Hybrid Light-Matter System
• Topological phases of many-body non-Hermitian systems
• Experimentally Probing Non-Hermitian Spectral Transition and Eigenstate Skewness
• Topological and fractal defect states in non-Hermitian lattices
• PT-symmetric Non-Hermitian Hopf Metal
• An Explicit Wavefunction of the Interacting Non-Hermitian Spin-1/2 1D System
• Coherent transfer of topological domain walls
• Non-Hermitian Hopf insulators
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• Extracting the internal nonlocality from the dilated Hermiticity
• The quantum phase transitions of dimer chain driven by an imaginary ac field
• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
• Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian
• Entanglement phases and phase transitions in monitored free fermion system due to localizations
• Experimental observation of energy-band Riemann surface
• Zero modes of velocity field and topological invariant in quantum torus
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Topological Photonic Systems: Virtuous Platforms to Study Topological Quantum Matter
• Non-Hermitian Topoelectrical Circuits: Expedient Tools for Topological State Engineering with Gain-Loss Modulation
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Non-Hermitian higher-order topological insulators enabled by altermagnet engineering
• Continuous phase transition induced by non-Hermiticity in the quantum contact process model
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
• Tailoring higher-order van Hove singularities in non-Hermitian interface systems via Floquet engineering
• Emergent dynamical quantum phase transition in a $Z_3$ symmetric chiral clock model
• A Hermitian bypass to the non-Hermitian quantum theory
• Anti-parity-time topologically undefined state
• Tailoring Corner States and Exceptional Points in Altermagnets
• Non-Hermitian topological wall modes in rotating Rayleigh-Benard convection
• Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Dynamical transition in non-Hermitian Chern insulator
• Topological invariant of velocity field in quantum systems
• Adiabatic charge transport through non-Bloch bands
• Disorder-driven exceptional points and concurrent topological phase transitions in non-Hermitian systems
• Quantum-vacuum-protected topological edge polaritons
• Optimal spectral transport of non-Hermitian systems
• Topological Phase Transitions and Edge-State Transfer in Time-Multiplexed Quantum Walks
• Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Dynamical non-Hermitian systems: Fingerprints and pure dephasing induced protection effect
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Algebraic States in Continuum in $d>1$ Dimensional Non-Hermitian Systems
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• Non-Markovianity Benefits Quantum Dynamics Simulation
• Exceptional flat bands in bipartite non-Hermitian lattices
• Robust interface-state laser in non-Hermitian micro-resonator arrays
• Interacting many-body non-Hermitian systems as Markov chains
• Braiding of dynamical eigenvalues of Hermitian bosonic Kitaev chains
• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field
• Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Anomalous Point-Gap Interactions Unveil the Mirage Bath
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• Spread complexity and localization in $\mathcal{P}\mathcal{T}$-symmetric systems
• Hall conductance of a non-Hermitian two-band system with k-dependent decay rates
• Non-Hermitian Effects in the Su-Schrieffer-Heeger model: Exploring Substrate Coupling and Decoupling Dynamics
• Topological Classification of Gapped/Gap-preserving Rational Space-Time Crystal Systems
• Recurrence method in Non-Hermitian Systems
• Self-healing of non-Hermitian topological skin modes
• Supermetal-insulator transition in a non-Hermitian network model
• Mechanical activity and odd elasticity of passive, 2D chiral metamaterials
• Non-Hermitian Higher-Order Weyl Semimetals
• Interferometric Geometric Phases of $\mathcal{P}\mathcal{T}$-symmetric Quantum Mechanics
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
• Beyond characteristic equations: A unified one-dimensional non-Bloch band theory via wavefunction data
• Winding-control mechanism of non-Hermitian systems
• Floquet topological properties in the Non-Hermitian long-range system with complex hopping amplitudes