Non-Hermitian skin effect beyond the tight-binding models

Abstract

The energy bands of non-Hermitian systems exhibit nontrivial topological features that arise from the complex nature of the energy spectrum. Under periodic boundary conditions (PBC), the energy spectrum describes rather generally closed loops in complex plane, characterized by integer nonzero winding numbers. Such nontrivial winding provides the topological signature of the non-Hermitian skin effect (NHSE), i.e. the macroscopic condensation of bulk states at the lattice edges under open boundary conditions (OBC). In spite of the great relevance of band winding in the non-Hermitian topological band theory and the related NHSE, most of current results rely on tight-binding models of non-Hermitian systems, while exact Bloch wave function analysis of the NHSE and related topological band theory is still lacking. While tight-binding models can correctly describe narrow-band electronic states with a relatively weak degree non-Hermiticity, they are not suited to describe high-energy wide-band electronic states and/or regimes corresponding to strong non-Hermiticity. Here we consider the single-particle continuous Schrödinger equation in a periodic potential, in which non-Hermiticity is introduced by an imaginary vector potential in the equation, and show that the NHSE is ubiquitous under OBC and characterized by a non-vanishing integer winding number, even thought the energy spectrum under PBC always comprises an open curve, corresponding to high-energy electronic states. We also show that the interior of the PBC energy spectrum corresponds to the complex eigenenergies sustaining localized (edge) states under semi-infinite boundary conditions.

arXiv comment12 pages, 8 figures, to appear in Phys. Rev. B

References in corpus (89)

• Topological Insulators
• Supersymmetry and Quantum Mechanics
• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• 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
• 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
• Non-Hermitian Chern bands
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Non-Hermitian Boundary Modes
• 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
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Non-Hermitian Topological Invariants in Real Space
• Critical non-Hermitian Skin Effect
• Topological phase transition in non-Hermitian quasicrystals
• Reciprocal skin effect and its realization in a topolectrical circuit
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Higher-order non-Hermitian skin effect
• New topological invariants in non-Hermitian systems
• Observation of arbitrary topological windings of a non-Hermitian band
• Non-Hermitian Delocalization and Eigenfunctions
• Robust light transport in non-Hermitian photonic lattices
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Observation of non-Bloch parity-time symmetry and exceptional points
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Spectral singularities and Bragg scattering in complex crystals
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Tenfold Way for Quadratic Lindbladians
• Second-order topological non-Hermitian skin effects
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Distribution of Eigenvalues in Non-Hermitian Anderson Model
• Non-Bloch band collapse and chiral Zener tunneling
• Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Skin effect and winding number in disordered non-Hermitian systems
• Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
• Non-Hermitian gauged topological laser arrays
• Generalized bulk-edge correspondence for non-hermitian topological systems
• Topological classification of non-Hermitian systems with reflection symmetry
• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Non-Hermitian second-order skin and topological modes
• Theory of directed localization in one dimension
• Winding Numbers, Complex Currents, and Non-Hermitian Localization
• Defective Edge States and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Non-Hermitian Skin Effects in Hermitian Correlated/Disordered Systems: Boundary-Sensitive/Insensitive Quantities and Pseudo Quantum Number
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Non-Bloch band theory in bosonic Bogoliubov-de Gennes systems
• Non-Bloch $\mathcal{P}\mathcal{T}$ symmetry breaking in non-Hermitian Photonic Quantum Walks
• Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System
• Ultrafast and Anharmonic Rabi Oscillations between Non-Bloch-Bands
• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
• Non-Hermitian band topology with generalized inversion symmetry
• Real space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems
• Curving the space by non-Hermiticity
• Unsupervised Learning of Non-Hermitian Topological Phases
• Non-Hermitian spectra and Anderson localization
• Supersymmetric transparent optical intersections
• Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling
• Localization-delocalization transition in disordered systems with a direction
• Localization in non-Hermitian quantum mechanics and flux-line pinning in superconductors
• Lamé polynomials, hyperelliptic reductions and Lamé band structure
• Stochastic non-Hermitian skin effect
• Delocalization in an open one-dimensional chain in an imaginary vector potential
• Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems
• Localization in an imaginary vector potential
• Hatano-Nelson model with a periodic potential
• Non-Hermitian topological phase transitions in superlattices and the optical Dirac equation
• Anyonic $\mathcal{P}\mathcal{T}$ symmetry, drifting potentials and non-Hermitian delocalization
• An exactly soluble model of a shallow double well

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• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
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• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Filling up complex spectral regions through non-Hermitian disordered chains
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• Quantum walks of correlated photons in non-Hermitian photonic lattices
• Non-Hermitian Hartman effect
• Bulk-edge correspondence and trapping at a non-Hermitian topological interface
• Investigation of a non-Hermitian edge burst with time-dependent perturbation theory
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Non-Hermitian skin effect and lasing of absorbing open-boundary modes in photonic crystals
• Real spectra in one-dimensional single-band non-Hermitian Hamiltonians
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect
• Optical non-Hermitian skin effect in two-dimensional uniform media
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Recurrence method in Non-Hermitian Systems
• Observation of non-Hermitian point gap in photonic crystals
• Self-healing of non-Hermitian topological skin modes