Topological states of non-Hermitian systems

Abstract

Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through non-Hermitian Hamiltonians appear in the context of photonic systems, where one needs to account for gain and loss, circuits of resonators, and also when modeling the lifetime due to interactions in condensed matter systems. Here we provide a brief overview of this rapidly growing subject, the search for topological states and a bulk-boundary correspondence in non-Hermitian systems.

Invited short review for the special issue "Topological States of Matter: Theory and Applications"

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• Non-Hermitean Localization and De-Localization
• Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
• Topological phase in a non-Hermitian PT symmetric system
• Dynamical quantum phase transitions in non-Hermitian lattices
• Relation between $\mathcal{P}\mathcal{T}$-symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models
• Non-Hermitian Topological Theory of Finite-Lifetime Quasiparticles: Prediction of Bulk Fermi Arc Due to Exceptional Point
• Topology of density matrices
• Dissipative preparation of Chern insulators
• Aharonov-Bohm photonic cages in waveguide and coupled resonator lattices by synthetic magnetic fields
• Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
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• Unified bulk-boundary correspondence for band insulators
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• Non-Hermitian Localization in Biological Networks
• Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
• Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model
• Flat bands in lattices with non-Hermitian coupling
• Chiral state-conversion without encircling an exceptional point
• Surface and 3D quantum Hall effects from engineering of exceptional points in nodal-line semimetals
• Su-Schrieffer-Heeger chain with one pair of PT-symmetric defects
• Resonances in open quantum systems
• Majorana Edge Modes with Gain and Loss
• Analysis of multiple exceptional points related to three interacting eigenmodes in a non-Hermitian Hamiltonian
• Topological protection from exceptional points in Weyl and nodal line semimetals
• Topologically protected modes in non-equilibrium stochastic systems
• PT Symmetric Floquet Topological Phase
• Clustering of exceptional points and dynamical phase transitions
• One-way transport in laser-illuminated bilayer graphene: A Floquet isolator
• PT Symmetric Floquet Topological Phase in SSH Model
• Crafting zero-bias one-way transport of charge and spin
• Towards a Floquet-Network Theory of Non-Reciprocal Transport
• Survival, decay, and topological protection in non-Hermitian quantum transport
• Exceptional points in quantum and classical dynamics
• Non-Hermitian Floquet invisibility
• Antiresonance induced by symmetry-broken contacts in quasi-one-dimensional lattices
• Reconfiguration of quantum states in $\mathcal{P}T$-symmetric quasi-one dimensional lattices
• Topological dynamics in an optomechanical system with highly non-degenerate modes

Cited by in corpus (190)

• Topological Photonics
• Exceptional Topology of Non-Hermitian Systems
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Non-Hermitian Boundary Modes
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Non-Hermitian Topological Invariants in Real Space
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• New topological invariants in non-Hermitian systems
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Higher-order topological corner states induced by gain and loss
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Symmetry-protected nodal phases in non-Hermitian systems
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Knots and Non-Hermitian Bloch Bands
• Second-order topological non-Hermitian skin effects
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Topological framework for directional amplification in driven-dissipative cavity arrays
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Perspective on topological states of non-Hermitian lattices
• Non-Bloch band collapse and chiral Zener tunneling
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Skin effect and winding number in disordered non-Hermitian systems
• Edge states in trimer lattices
• Knotted Non-Hermitian Metals
• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Fermion doubling theorems in 2D non-Hermitian systems for Fermi points and exceptional points
• Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
• A perspective on topological nanophotonics: current status and future challenges
• Topological classification of non-Hermitian systems with reflection symmetry
• Tutorial: Computing topological invariants in two-dimensional photonic crystals
• Non-Hermitian exceptional Landau quantization in electric circuits
• Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
• Bulk-boundary correspondence for non-Hermitian Hamiltonians via Green functions
• Non-Hermitian Weyl Physics in Topological Insulator Ferromagnet Junctions
• Many-body approach to non-Hermitian physics in fermionic systems
• Guided accumulation of active particles by topological design of a second-order skin effect
• Defective Edge States and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals
• Observation of non-Hermitian topology with non-unitary dynamics of solid-state spins
• Non-trivial point-gap topology and non-Hermitian skin effect in photonic crystals
• Non-Hermitian topology of spontaneous magnon decay
• Topological states in non-Hermitian two-dimensional Su-Schrieffer-Heeger model
• Topological classification of non-Hermitian bands
• Non-Hermitian physics and master equations
• Nonlinearity induced topological physics in momentum space and real space
• Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
• Knot topology of exceptional point and non-Hermitian no-go theorem
• Topological phases and nonreciprocal edge states in non-Hermitian Floquet Insulators
• Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions
• Magnetic suppression of non-Hermitian skin effects
• Topological theory of non-Hermitian photonic systems
• Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices
• Topological phases in ring resonators: recent progress and future prospects
• Non-Hermitian Topological Phases: Principles and Prospects
• Universality in driven open quantum matter
• Topological phases of polaritons in a cavity waveguide
• Dynamical characterization of non-Hermitian Floquet topological phases in one-dimension
• Bulk-edge correspondence and long range hopping in the topological plasmonic chain
• Finite-size effects in non-Hermitian topological systems
• Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
• Non-Hermitian skin effect as an impurity problem
• Topological Phase Transition Independent of System Non-Hermiticity
• Topological phonon polaritons in one-dimensional non-Hermitian nanoparticle chains
• Dual topological characterization of non-Hermitian Floquet phases
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Non-Hermitian skin effect of dislocations and its topological origin
• Non-Hermitian Floquet Topological Matter -- A Review
• Exceptional points and the topology of quantum many-body spectra
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Non-Hermitian topological phases and dynamical quantum phase transitions: A generic connection
• Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems
• Helical Liquids in Semiconductors
• Non-Hermitian Topological End-Mode Lasing in Polariton Systems
• Symmetry and topological classification of Floquet non-Hermitian systems
• Geometry-dependent skin effects in reciprocal photonic crystals
• Non-Hermitian Dynamic Strings and Anomalous Topological Degeneracy on non-Hermitian Toric-code Model with Parity-time Symmetry
• Non-Hermitian scattering on a tight-binding lattice
• Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling
• Inversion symmetric non-Hermitian Chern insulator
• Non-Hermitian anomalous skin effect
• Non-Hermitian topology in monitored quantum circuits
• Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics
• Spontaneous topological pumping in non-Hermitian systems
• Controlling Exceptional Points with Light
• Non-Hermitian skin effect edge
• Extended Bloch theorem for topological lattice models with open boundaries
• Diagnosis of bulk phase diagram of non-reciprocal topological lattices by impurity modes
• Exponentially growing bulk Green functions as signature of nontrivial non-Hermitian winding number in one dimension
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Radiative topological biphoton states in modulated qubit arrays
• Quantum dynamics on a lossy non-Hermitian lattice
• Hyperbolic Nodal Band Structures and Knot Invariants
• Topological phase in plasma physics
• Light-driven Lifshitz transitions in non-Hermitian multi-Weyl semimetals
• Topological edge-states of the PT-symmetric Su-Schrieffer-Heeger model: An effective two-state description
• Quantized Angular Momentum in Topological Optical Systems
• Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems
• Non-Hermitian skin effect induced by Rashba-Dresselhaus spin-orbit coupling
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Non-Hermitian CT-Symmetric Spectral Protection of Nonlinear Defect Modes
• Loschmidt echo and fidelity decay near an exceptional point
• Topological Protection in non-Hermitian Haldane Honeycomb Lattices
• Non-Hermitian impurities in Dirac systems
• Non-linear dynamics of the non-Hermitian Su-Schrieffer-Heeger model
• Irrational Non-Abelian Statistics for Non-Hermitian Generalization of Majorana Zero Modes
• Hexagonally warped exceptional physics in multi-Weyl semimetals
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
• Polaritonic Tamm states induced by cavity photons
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Non-hermitian topology in multiterminal superconducting junctions
• Non-Hermitian topological mobility edges and transport in photonic quantum walks
• Topological Signatures in Quantum Transport in Anomalous Floquet-Anderson Insulators
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Exceptional points in oligomer chains
• $S$-matrix pole symmetries for non-Hermitian scattering Hamiltonians
• Non-Hermiticity induced Exceptional Points and Skin Effect in the Dice-Haldane Model
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Non-Hermitian second-order topological superconductors
• A renormalization group approach to non-Hermitian topological quantum criticality
• Non-Hermitian chiral anomalies
• Long-lived elementary excitations and light coherence in topological lasers
• Anomalous features of non-Hermitian topological states
• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Non-Hermitian Avalanche Effect: Non-Perturbative Effect Induced by Local Non-Hermitian Perturbation on a Z2 Topological Order
• Characterizing and Tuning Exceptional Points Using Newton Polygons
• Dynamical signatures of point-gap Weyl semimetal
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Alice string in Non-Hermitian Systems
• Point-Gap Bound States in Non-Hermitian Systems
• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
• State-dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Topological circuit of a versatile non-Hermitian quantum system
• Spectral and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric tight-binding chain with gain and loss
• Edge states in a non-Hermitian topological crystalline insulator
• Eigenstate clustering around exceptional points
• Non-Hermitian semi-Dirac semi-metals
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Non-Bloch dynamics and topology in a classical non-equilibrium process
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Topological invariants of complex energy plane in non-Hermitian systems
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• Defective Edge states and Anomalous Bulk-boundary Correspondence for Topological Insulators under Non-Hermitian Similarity Transformation
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Emergent $\mathcal{P}\mathcal{T}$-symmetry breaking of collective modes with topological critical phenomena
• Topological states at exceptional points
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Quasi-stationary solutions in non-Hermitian systems
• Tunable chiral anomalies and coherent transport on a honeycomb lattice
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• Topological characteristics of gap closing points in nonlinear Weyl semimetals
• Lasing condition for trapped modes in subwavelength--wired PT--symmetric resonators
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Local Non-Hermitian Hamiltonian Formalism for Dissipative Fermionic Systems and Loss-Induced Population Increase in Fermi Superfluids
• Robust nonequilibrium edge currents with and without band topology
• The quantum phase transitions of dimer chain driven by an imaginary ac field
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping
• Propagation of light through amplifying honeycomb photonic lattice
• Topological invariant of velocity field in quantum systems
• Exploring Metamaterial Lasers through Non-Hermitian Scattering Formalism
• Non-Hermitian magnetic moment
• A Hermitian bypass to the non-Hermitian quantum theory
• Real spectra and phase transition of skin effect in nonreciprocal systems
• 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
• Determining non-Hermitian parent Hamiltonian from a single eigenstate
• One-directional polarization transport in electron/nuclear spin chains with loss and gain
• Supermetal-insulator transition in a non-Hermitian network model
• Non-Hermitian Gravitational Wave Scattering
• Magnetic field effects on the Kitaev model coupled to environment
• Exploring Spectral Singularities in Dirac Semimetals: The Role of Non-Hermitian Physics and Dichroism
• Correspondence between non-Hermitian topology and directional amplification in the presence of disorder
• Zero Indirect Band Gap in Non-Hermitian Systems
• Phase transition from Weyl to self-linked semimetal using bi-circular laser
• Non-Hermitian Higher-Order Dirac Semimetals
• $q$th-root non-Hermitian Floquet topological insulators
• A new Berry phase term in parity-time symmetric non-Hermitian spin-1/2 quantum systems