Topological Non-Hermitian skin effect

Abstract

This article reviews recent developments in the non-Hermitian skin effect (NHSE), particularly on its rich interplay with topology. The review starts off with a pedagogical introduction on the modified bulk-boundary correspondence, the synergy and hybridization of NHSE and band topology in higher dimensions, as well as, the associated topology on the complex energy plane such as spectral winding topology and spectral graph topology. Following which, emerging topics are introduced such as non-Hermitian criticality, dynamical NHSE phenomena, and the manifestation of NHSE beyond the traditional linear non-interacting crystal lattices, particularly its interplay with quantum many-body interactions. Finally, we survey the recent demonstrations and experimental proposals of NHSE.

A review article with 38 pages and 17 figures. Comments are welcome. Note: this arxiv version is an experimental "living'' review article that will be continually updated to keep abreast of recent developments in the field. Please cite the published version of this review at https://link.springer.com/article/10.1007/s11467-023-1309-z

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• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Knotted Non-Hermitian Metals
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• Impurity induced scale-free localization
• Nodal Loop and Nodal Surface States in Ti3Al Family Materials
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• Floquet second-order topological insulators in non-Hermitian systems
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• Electromagnetic response of quantum Hall systems in dimensions five and six and beyond
• Free-fermion Entanglement Spectrum through Wannier Interpolation
• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
• Floquet Mechanism for Non-Abelian Fractional Quantum Hall States
• Non-Hermitian skin effect as an impurity problem
• Non-Hermitian band topology with generalized inversion symmetry
• Optimal decay of Wannier functions in Chern and Quantum Hall insulators
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Engineering Non-Hermitian Skin Effect with Band Topology in Ultracold Gases
• Non-Hermitian skin effect of dislocations and its topological origin
• Dual topological characterization of non-Hermitian Floquet phases
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• Nonlinear non-Hermitian skin effect
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• Symmetry and topological classification of Floquet non-Hermitian systems
• Quantum Entanglement of Non-Hermitian Quasicrystals
• Unconventional scaling at non-Hermitian critical points
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• Non-Hermitian Squeezed Polarons
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Theoretical Prediction of Non-Hermitian Skin Effect in Ultracold Atom Systems
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• Anomalous Behaviors of Quantum Emitters in Non-Hermitian Baths
• From the topological spin-Hall effect to the non-Hermitian skin effect in an elliptical micropillar chain
• From triple-point materials to multiband nodal links
• Topological spin excitations in non-Hermitian spin chains with a generalized kernel polynomial algorithm
• Nonreciprocal Charge and Spin Transport Induced by Non-Hermitian Skin Effect in Mesoscopic Heterojunctions
• Non-Hermitian elastic waveguides with piezoelectric feedback actuation: non-reciprocal bands and skin modes
• Topological energy braiding of the non-Bloch bands
• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Topology in non-Hermitian Chern insulators with skin effect
• Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics
• Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
• Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures
• Dynamic skin effects in non-Hermitian systems
• System size dependent topological zero modes in coupled topolectrical chains
• R-DMFT study of a non-Hermitian skin effect for correlated systems: analysis based on a pseudo-spectrum
• Cyclotron quantization and mirror-time transition on nonreciprocal lattices
• Non-Bloch quench dynamics
• Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric
• Compatibility of transport effects in non-Hermitian nonreciprocal systems
• Non-Hermitian boundary spectral winding
• Solvable non-Hermitian skin effect in many-body unitary dynamics
• Light-induced phase crossovers in a quantum spin Hall system
• Manipulating non-Hermitian skin effect via electric fields
• Terahertz Polarization Conversion from Optical Dichroism in a Topological Dirac Semimetal
• Anatomy of open-boundary bulk in multiband non-Hermitian systems
• Stochastic non-Hermitian skin effect
• Enhanced higher harmonic generation from nodal topology
• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
• Phase transitions of non-Abelian charged nodal links in a spring-mass system
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• Entanglement, non-Hermiticity, and duality
• Non-Hermitian Weyl semimetal and its Floquet engineering
• Hyperbolic Nodal Band Structures and Knot Invariants
• Non-Hermitian topology in rock-paper-scissors games
• Direction reversal of non-Hermitian skin effect via coherent coupling
• Non-Hermitian topological end breathers
• Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems
• Degeneracy and defectiveness in non-Hermitian systems with open boundary
• Skin effect and dynamical delocalization in non-Hermitian quasicrystals with spin-orbit interaction
• Two-dimensional quantum walk with non-Hermitian skin effects
• Full counting statistics in the many-body Hatano-Nelson model
• Topological insulating phases from two-dimensional nodal loop semimetals
• Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation
• Non-Hermitian topological mobility edges and transport in photonic quantum walks
• Engineering topological phases with a three-dimensional nodal-loop semimetal
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Filling up complex spectral regions through non-Hermitian disordered chains
• Non-Hermitian topological exciton-polariton corner modes
• $2\pi$-flux loop semimetals
• A renormalization group approach to non-Hermitian topological quantum criticality
• Non-Hermitian chiral anomalies
• Non-Hermitian Hartman effect
• Floquet Topological Semimetal with Nodal Helix
• Non-Hermitian skin effect in a spin-orbit-coupled Bose-Einstein condensate
• Optomechanically induced transparency and directional amplification in a non-Hermitian optomechanical lattice
• Non-Bloch PT symmetry breaking: Universal threshold and dimensional surprise
• Bulk-edge correspondence and trapping at a non-Hermitian topological interface
• Anisotropic non-linear optical response of nodal loop materials
• Hermitian chiral boundary states in non-Hermitian topological insulators
• Critical and non critical non-Hermitian topological phase transitions in one dimensional chains
• Fundamental constraints on the observability of non-Hermitian effects in passive systems
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
• Space-Time Duality between Quantum Chaos and Non-Hermitian Boundary Effect
• Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems
• Unsupervised identification of Floquet topological phase boundaries
• Magnetic Flux Response of Non-Hermitian Topological Phases
• Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect
• Concentrated subradiant modes in one-dimensional atomic array coupled with chiral waveguides
• Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems
• Electronic polarization in non-Bloch band theory
• Anomalous hybridization of spectral winding topology in quantized steady-state responses
• Chiral Hinge Transport in Disordered Non-Hermitian Second-Order Topological Insulators
• Duality between Generalized Non-Hermitian HN Model in Flat Space and Hermitian System in Curved space
• Nonlinear topological Toda quasicrystal

Cited by in corpus (151)

• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Floquet engineering of point-gapped topological superconductors
• Dimensional transmutation from non-Hermiticity
• Non-Hermitian Mott Skin Effect
• Non-Hermitian Floquet Topological Matter -- A Review
• Non-Hermitian Chiral Skin Effect
• Observation of the non-Hermitian skin effect and Fermi skin on a digital quantum computer
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Many-Body Non-Hermitian Skin Effect for Multipoles
• Nonlinear Non-Hermitian Skin Effect and Skin Solitons in Temporal Photonic Feedforward Lattices
• Occupation-dependent particle separation in one-dimensional non-Hermitian lattices
• Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators
• Many-body non-Hermitian skin effect under dynamic gauge coupling
• Skin modes in a nonlinear Hatano-Nelson model
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Magnetochiral Charge Pumping due to Charge Trapping and Skin Effect in Chirality-Induced Spin Selectivity
• Erratic non-Hermitian skin localization
• Anderson transition at complex energies in one-dimensional parity-time-symmetric disordered systems
• Exact analogue of the Hatano-Nelson model in 1D continuous nonreciprocal systems
• Incoherent non-Hermitian skin effect in photonic quantum walks
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Observation of scale-free localized states induced by non-Hermitian defects
• Percolation-induced PT symmetry breaking
• A brief review of hybrid skin-topological effect
• Edge theory of non-Hermitian skin modes in higher dimensions
• Green's functions of multiband non-Hermitian systems
• Breaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides
• Non-reciprocal dynamics and the non-Hermitian skin effect of repulsively bound pairs
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Accelerating Relaxation Dynamics in Open Quantum System with Liouvillian Skin Effect
• Dissipative Boundary State Preparation
• Non-Hermitian Second-Order Topological Phases and Bipolar Skin Effect in Photonic Kagome Crystals
• Entanglement phase transition due to reciprocity breaking without measurement or post-selection
• Non-Bloch band theory for non-Hermitian continuum systems
• Self acceleration from spectral geometry in dissipative quantum-walk dynamics
• Non-Hermitian Skin Effect in Periodically-Driven Dissipative Ultracold Atoms
• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Steady-state edge burst: From free-particle systems to interaction-induced phenomena
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Dynamical suppression of many-body non-Hermitian skin effect in Anyonic systems
• Non-Hermitian extended midgap states and bound states in the continuum
• Non-Hermitian second-order topological superconductors
• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Spectral structure and doublon dissociation in the two-particle non-Hermitian Hubbard model
• Observation of disorder-induced boundary localization
• Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Boundary sensitive Lindbladians and relaxation dynamics
• Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization
• Liouvillian skin effects and fragmented condensates in an integrable dissipative Bose-Hubbard model
• Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field
• Nonsymmetric evanescent coupling in photonics
• Stable many-body localization under random continuous measurements in the no-click limit
• Non-Markovian skin effect
• Observation of Impurity-Induced Scale-Free Localization in a Disordered Non-Hermitian Electrical Circuit
• Higher-order Skin Effect through a Hermitian-non-Hermitian Correspondence and Its Observation in an Acoustic Kagome Lattice
• Real-space topological localizer index to fully characterize the dislocation skin effect
• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• Biorthogonal topological charge pumping in non-Hermitian systems
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Universal spectral moment theorem and its applications in non-Hermitian systems
• Tunable Aharonov-Bohm cages through anti-$\mathcal{P}\mathcal{T}$-symmetric imaginary couplings
• Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Harnessing Nonlinearity to Tame Wave Dynamics in Nonreciprocal Active Systems
• Non-Hermitian generalizations of the Yao-Lee model augmented by SO(3)-symmetry-breaking terms
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Non-Hermitian superconducting diode effect
• Entangelment Entropy on Generalized Brillouin Zone
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Quantum Sensing with Driven-Dissipative Su-Schrieffer-Heeger Lattices
• Non-Bloch band theory for time-modulated discrete mechanical systems
• Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems
• Non-Bloch Dirac Points and Phase Diagram in the Stacked Non-Hermitian SSH Model
• Experimental probe of band structures of bilayer valley photonic crystals
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Topology of Discrete Quantum Feedback Control
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Impurity-induced counter skin-effect and linear modes in non-Hermitian systems
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Inverse Design of Winding Tuple for Non-Hermitian Topological Edge Modes
• Two-dimensional lattice with an imaginary magnetic field
• Boundary-driven many-body phase transitions in a non-Hermitian disordered fermionic chain
• Nodal phases in non-Hermitian wallpaper crystals
• Exact density profile in a tight-binding chain with dephasing noise
• Liouvillian skin effect in quantum neural networks
• Topological, multi-mode amplification induced by non-reciprocal, long-range dissipative couplings
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Winding Topology of Multifold Exceptional Points
• Non-Hermitian dynamical topological winding in photonic mesh lattices
• Manipulating Spectral Windings and Skin Modes through Nonconservative Couplings
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Non-Hermitian theory of valley excitons in two-dimensional semiconductors
• Non-Hermitian Boundary in a Surface Selective Reconstructed Magnetic Weyl Semimetal
• Space-time symmetry and nonreciprocal parametric resonance in mechanical systems
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Quantum Pontus-Mpemba Effect Enabled by the Liouvillian Skin Effect
• Antichiral and trap-skin dynamics in a nonreciprocal bosonic two-leg ladder with artificial magnetic flux
• Tentaclelike spectra and bound states in Hatano-Nelson chain with long-range impurity coupling
• Topologically protected negative entanglement
• Exceptional deficiency of non-Hermitian systems
• Topological Dynamics and Correspondences in Composite Exceptional Rings
• Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system
• Convection-modulated topological edge mode and extended-localized criticality in thermal metamaterials
• Hermitian and non-Hermitian topology in active matter
• Gauge Field Induced Unconventional Skin Effect in Spinful Non-Hermitian Systems
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• Wave propagation in an elastic lattice with non-reciprocal stiffness and engineered damping
• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
• Dynamic transition of the density-matrix topology under parity-time symmetry
• Topological and fractal defect states in non-Hermitian lattices
• Fidelity zeros and Lee-Yang theory of quantum phase transitions
• Tailoring higher-order van Hove singularities in non-Hermitian interface systems via Floquet engineering
• Intrinsic non-Hermitian topological phases
• Adiabatic charge transport through non-Bloch bands
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Solution of Wave Acceleration and Non-Hermitian Jump in Nonreciprocal Lattices
• Non-Hermitian higher-order topological insulators enabled by altermagnet engineering
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Tailoring Corner States and Exceptional Points in Altermagnets
• Dynamical non-Hermitian systems: Fingerprints and pure dephasing induced protection effect
• Disorder-driven exceptional points and concurrent topological phase transitions in non-Hermitian systems
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Emergence of Imaginary Time Crystals in the non-Hermitian Su-Schrieffer-Heeger model
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal
• Insensitive nonreciprocal edge breathers
• Interacting many-body non-Hermitian systems as Markov chains
• Topology of the generalized Brillouin zone of one-dimensional models
• Precision-Induced Irreversibility in non-Hermitian systems
• Liouvillian topology and nonreciprocal dynamics in open Floquet chains
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
• Coupled-wire construction of non-Abelian higher-order topological phases
• Spread complexity and localization in $\mathcal{P}\mathcal{T}$-symmetric systems
• Magnetic field effects on the Kitaev model coupled to environment
• Exponential $U(1)$ Symmetry-Breaking Phase as a Disorder-Free Quantum Glass
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Exceptional Luttinger Liquids from sublattice dependent interaction