Correspondence between winding numbers and skin modes in non-hermitian systems

Abstract

We establish exact relations between the winding of "energy" (eigenvalue of Hamiltonian) on the complex plane as momentum traverses the Brillouin zone with periodic boundary condition, and the presence of "skin modes" with open boundary condition in non-hermitian systems. We show that the nonzero winding with respect to any complex reference energy leads to the presence of skin modes, and vice versa. We also show that both the nonzero winding and the presence of skin modes share the common physical origin that is the non-vanishing current through the system.

arXiv comment22 pages, 10 figures. To appear in Physical Review Letters

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• One-dimensional non-Hermitian band structures as Riemann surfaces
• Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Chiral Dissociation of Bound Photon Pairs for a Non-Hermitian Skin Effect
• Exceptional second-order topological insulators
• Topology and its detection in a dissipative Aharonov-Bohm chain
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Theory for the spectral splitting exponent of exceptional points
• Quantum Pontus-Mpemba Effect Enabled by the Liouvillian Skin Effect
• Bulk-boundary correspondence in topological systems with the momentum dependent energy shift
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
• $K$-theory classification of Wannier localizability and detachable topological boundary states
• 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
• Winding Topology of Multifold Exceptional Points
• Impurity in a Fermi gas under non-Hermitian spin-orbit coupling
• Manipulating Spectral Windings and Skin Modes through Nonconservative Couplings
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Discriminant indicator with generalized rotational symmetry
• Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Alternating quantum-emitter chains: Exceptional-point phase transition, edge state, and quantum walks
• Topologically protected negative entanglement
• Supercurrent from the imaginary part of the Andreev levels in non-Hermitian Josephson junctions
• Topological phases of many-body non-Hermitian systems
• Exceptional deficiency of non-Hermitian systems
• Topological extension including quantum jump
• Hermitian and non-Hermitian topology in active matter
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system
• Controllable suppression of Non-Hermitian skin effects
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Non-Hermitian skin effect and electronic nonlocal transport
• Gauge Field Induced Unconventional Skin Effect in Spinful Non-Hermitian Systems
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems
• The quantum phase transitions of dimer chain driven by an imaginary ac field
• Topological and fractal defect states in non-Hermitian lattices
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• An Explicit Wavefunction of the Interacting Non-Hermitian Spin-1/2 1D System
• High-fidelity multipartite entanglement creation in non-Hermitian qubits
• Experimentally Probing Non-Hermitian Spectral Transition and Eigenstate Skewness
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• Non-Hermitian Hopf insulators
• Exceptional mode topological surface laser
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
• From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
• Exceptionally deficient topological square-root insulators
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Fidelity zeros and Lee-Yang theory of quantum phase transitions
• Experimental observation of energy-band Riemann surface
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• An unusual phase transition in a non-Hermitian Su-Schrieffer-Heeger model
• PT-symmetric Non-Hermitian Hopf Metal
• Topological spin textures in electronic non-Hermitian systems
• Topological Phase Transitions and Edge-State Transfer in Time-Multiplexed Quantum Walks
• Non-Hermitian higher-order topological insulators enabled by altermagnet engineering
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains
• Inter-species topological phases via a dynamical gauge field
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Intrinsic non-Hermitian topological phases
• Optimal spectral transport of non-Hermitian systems
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Symmetry and Topology of Monitored Quantum Dynamics
• Topological Amplification of the Bosonic Kitaev Chain with Non-Uniform Loss
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Dynamical transition in non-Hermitian Chern insulator
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Dynamical non-Hermitian systems: Fingerprints and pure dephasing induced protection effect
• Quantum-vacuum-protected topological edge polaritons
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems
• Non-Hermitian physics and topological phenomena in convective thermal metamaterials
• Topology of the generalized Brillouin zone of one-dimensional models
• Winding-control mechanism of non-Hermitian systems
• Braiding of dynamical eigenvalues of Hermitian bosonic Kitaev chains
• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field
• Symmetry and Topology of Successive Quantum Feedback Control
• 1D Spontaneous Symmetry Breaking in thermal equilibrium via Non-Hermitian Construction
• Observation of non-Hermitian point gap in photonic crystals
• Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping
• Scaling rule in critical non-Hermitian skin effect
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Algebraic States in Continuum in $d>1$ Dimensional Non-Hermitian Systems
• Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems
• Supermetal-insulator transition in a non-Hermitian network model
• Liouvillian topology and nonreciprocal dynamics in open Floquet chains
• Emulating non-Hermitian dynamics in a finite non-dissipative quantum system
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
• Emergence of Imaginary Time Crystals in the non-Hermitian Su-Schrieffer-Heeger model
• Emergence of Hermitian topology from non-Hermitian knots
• Anomalous Point-Gap Interactions Unveil the Mirage Bath
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• Algebraic skin effect in two-dimensional non-Hermitian metamaterials
• Self-healing of non-Hermitian topological skin modes
• Recurrence method in Non-Hermitian Systems