Non-Hermitian topological phenomena: A review

Abstract

The past decades have witnessed an explosion of interest in topological materials, and a lot of mathematical concepts have been introduced in condensed matter physics. Among them, the bulk-boundary correspondence is the central topic in topological physics, which has inspired researchers to focus on boundary physics. Recently, the concepts of topological phases have been extended to non-Hermitian Hamiltonians, whose eigenvalues can be complex. Besides the topology, non-Hermiticity can also cause a boundary phenomenon called the non-Hermitian skin effect, which is an extreme sensitivity of the spectrum to the boundary condition. In this article, we review developments in non-Hermitian topological physics by focusing mainly on the boundary problem. As well as the competition between non-Hermitian and topological boundary phenomena, we discuss the topological nature inherent in non-Hermiticity itself.

Review article submitted to Annual Review of Condensed Matter Physics (accepted); 31 pages, 5 figures

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• Floquet engineering of point-gapped topological superconductors
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• Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Nonreciprocal Synchronization of Active Quantum Spins
• Many-Body Non-Hermitian Skin Effect for Multipoles
• Hybrid higher-order skin-topological effect in hyperbolic lattices
• Universal platform of point-gap topological phases from topological materials
• Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport
• Observation of Quantum metric and non-Hermitian Berry curvature in a plasmonic lattice
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Skin modes in a nonlinear Hatano-Nelson model
• Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• Topological enhancement of non-normality in non-Hermitian skin effects
• Erratic non-Hermitian skin localization
• Magnetochiral Charge Pumping due to Charge Trapping and Skin Effect in Chirality-Induced Spin Selectivity
• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
• 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
• Non-Hermitian phase-biased Josephson junctions
• Edge theory of non-Hermitian skin modes in higher dimensions
• A brief review of hybrid skin-topological effect
• Percolation-induced PT symmetry breaking
• Breaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides
• The bosonic skin effect: boundary condensation in asymmetric transport
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• Non-Hermitian Topology in Hermitian Topological Matter
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• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
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• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Non-Hermitian extended midgap states and bound states in the continuum
• Non-Hermitian zero-energy pinning of Andreev and Majorana bound states in superconductor-semiconductor systems
• Field theory of non-Hermitian disordered systems
• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Exponentially Enhanced non-Hermitian Cooling
• Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
• From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Non-Unitary Quantum Many-Body Dynamics using the Faber Polynomial Method
• Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model
• Symmetric non-Hermitian skin effect with emergent nonlocal correspondence
• Stable many-body localization under random continuous measurements in the no-click limit
• Boundary sensitive Lindbladians and relaxation dynamics
• Pseudospin-orbit coupling and non-Hermitian effects in the Quantum Geometric Tensor of a plasmonic lattice
• Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization
• Liouvillian skin effects and fragmented condensates in an integrable dissipative Bose-Hubbard model
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Exact WKB analysis for $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics: Study of the Ai-Bender-Sarkar conjecture
• Nonsymmetric evanescent coupling in photonics
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• Transient amplification in stable Floquet media
• Quantum theory of non-Hermitian optical binding between nanoparticles
• Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point
• Non-Hermitian minimal Kitaev chains
• Real-space topological localizer index to fully characterize the dislocation skin effect
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{P}\mathcal{T}$ symmetry
• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Lindbladian dynamics with loss of quantum jumps
• Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation
• Phase Transitions in Nonreciprocal Driven-Dissipative Condensates
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Topological Phases of Tight-Binding Trimer Lattice in the BDI Symmetry Class
• Andreev non-Hermitian Hamiltonian for open Josephson junctions from Green's functions
• Autoregressive neural quantum states of Fermi Hubbard models
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Complex semiclassical theory for non-Hermitian quantum systems
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• Bulk-Edge Correspondence for Point-Gap Topological Phases in Junction Systems
• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
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• Lindbladian versus Postselected Non-Hermitian Topology
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• Real spectra in one-dimensional single-band non-Hermitian Hamiltonians
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Geometric contribution to adiabatic amplification in non-Hermitian systems
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• Accelerating multipartite entanglement generation in non-Hermitian superconducting qubits
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• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
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• Dissipation Enhanced Unidirectional Transport in Topological Systems
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• Topology of Discrete Quantum Feedback Control
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• Nodal phases in non-Hermitian wallpaper crystals
• Many-body critical non-Hermitian skin effect
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
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• Demonstration of a Tunable Non-Hermitian Nonlinear Microwave Dimer
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• Topological Operations Around Exceptional Points via Shortcuts to Adiabaticity
• Emergent Topology in Many-Body Dissipative Quantum Matter
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• Winding Topology of Multifold Exceptional Points
• Insights from the exact analytical solution of periodically driven transverse field Ising chain
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• Topological phases in discrete stochastic systems
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• Shock wave generation and propagation in dissipative and nonlocal nonlinear Rydberg media
• Gain engineering and atom lasing in a topological edge state in synthetic dimensions
• Topologically protected negative entanglement
• Exceptional deficiency of non-Hermitian systems
• Gauge Field Induced Unconventional Skin Effect in Spinful Non-Hermitian Systems
• Dissipative phase transition of interacting non-reciprocal fermions
• Fragmented exceptional points and their bulk and edge realizations in lattice models
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• Topological and fractal defect states in non-Hermitian lattices
• Magnon topology driven by altermagnetism
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• From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
• Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian
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• Noisy Stark probes as quantum-enhanced sensors
• Scaling of pseudospectra in exponentially sensitive lattices
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
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• Topological Amplification of the Bosonic Kitaev Chain with Non-Uniform Loss
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity
• Optimal spectral transport of non-Hermitian systems
• A Non-Hermitian State-to-State Analysis of Transport in Aggregates with Multiple Endpoints
• Disorder and non-Hermiticity in Kitaev spin liquids with a Majorana Fermi surface
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
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• Intrinsic non-Hermitian topological phases
• Multi-block exceptional points in open quantum systems
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• Insensitive nonreciprocal edge breathers
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• Coupled-wire construction of non-Abelian higher-order topological phases