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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Cited by in corpus (151)

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• 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
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• 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
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• 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
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• 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
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• Braiding Topology of Non-Hermitian Open-Boundary Bands
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• 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
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• 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
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• Liouvillian skin effect in quantum neural networks
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• Winding Topology of Multifold Exceptional Points
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• Non-Hermitian theory of valley excitons in two-dimensional semiconductors
• Non-Hermitian Boundary in a Surface Selective Reconstructed Magnetic Weyl Semimetal
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• 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
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• 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