New topological invariants in non-Hermitian systems

Abstract

Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in non-Hermitian Hamiltonians with relevant examples and realistic model setups. Discussions are devoted to both the adaptations of topological invariants from Hermitian to non-Hermitian systems, as well as origins of new topological invariants in the latter setup. Unique properties such as exceptional points and complex energy landscapes lead to new topological invariants including winding number/vorticity defined solely in the complex energy plane, and half-integer winding/Chern numbers. New forms of Kramers degeneracy appear here rendering distinct topological invariants. Modifications of adiabatic theory, time-evolution operator, biorthogonal bulk-boundary correspondence lead to unique features such as topological displacement of particles, `skin-effect', and edge-selective attenuated and amplified topological polarizations without chiral symmetry. Extension and realization of topological ideas in photonic systems are mentioned. We conclude with discussions on relevant future directions, and highlight potential applications of some of these unique topological features of the non-Hermitian Hamiltonians.

arXiv comment28 pages, 11 figures. Invited review article. Typos corrected

References in corpus (173)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Unpaired Majorana fermions in quantum wires
• Topological Insulators in Three Dimensions
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Making Sense of Non-Hermitian Hamiltonians
• Classification of topological quantum matter with symmetries
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Edge states and topological invariants of non-Hermitian systems
• Quantum Spin Hall Effect
• Quantized Electric Multipole Insulators
• Periodic table for topological insulators and superconductors
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Higher-Order Topological Insulators
• Topological superconductors: a review
• Colloquium: Topological Band Theory
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Band Theory for Non-Hermitian Hamiltonians
• Coherent Perfect Absorbers: Time-reversed Lasers
• Anomalous edge state in a non-Hermitian lattice
• Topological energy transfer in an optomechanical system with exceptional points
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• PT-symmetric laser-absorber
• Visualization of Branch Points in PT-Symmetric Waveguides
• Non-Hermitian Chern bands
• Topological nodal line semimetals with and without spin-orbital coupling
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Antiferromagnetic topological insulators
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• PT-Symmetric Phonon Laser
• Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
• Nodal-chain metals
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Second-order photonic topological insulator with corner states
• Pump-induced Exceptional Points in Lasers
• Edge states and topological phases in non-Hermitian systems
• Introduction to PT-Symmetric Quantum Theory
• Second-Order Topological Phases in Non-Hermitian Systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Topological Hybrid Silicon Microlasers
• Topologically protected midgap states in complex photonic lattices
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• $\mathcal{P}\mathcal{T}$-Symmetry-Breaking Chaos in Optomechanics
• Spin-orbit-free Weyl-loop and Weyl-point semimetals in a stable three-dimensional carbon allotrope
• PT symmetry and spontaneous symmetry breaking in a microwave billiard
• Classification of Topological Insulators and Superconductors
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Observation of an exceptional point in a chaotic optical microcavity
• Nodal-link semimetals
• Optomechanically-Induced Transparency in partiy-time-symmetric microresonators
• Topological states of non-Hermitian systems
• Robust light transport in non-Hermitian photonic lattices
• Stability of solitons in PT-symmetric couplers
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Majorana bound states from exceptional points in non-topological superconductors
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Topological invariance and global Berry phase in non-Hermitian systems
• Optical solitons in $\mathcal{P}\mathcal{T}$-symmetric nonlinear couplers with gain and loss
• Symmetry-protected nodal phases in non-Hermitian systems
• Topological Hopf and chain link semimetal states and their application to Co2MnGa (Theory and Materials Prediction)
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
• Simultaneous Observation of Topological Edge State and Exceptional Point in an Open and Non-Hermitian System
• The Chirality of Exceptional Points
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Nonlinearly-PT-symmetric systems: spontaneous symmetry breaking and transmission resonances
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Nodal-knot semimetals
• Anomalous helical edge states in a non-Hermitian Chern insulator
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Geometric phase around exceptional points
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Gain-Driven Discrete Breathers in PT-Symmetric Nonlinear Metamaterials
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Surfaces of Axion Insulators
• Parity-time-symmetric topological superconductor
• Mechanical PT symmetry in coupled optomechanical systems
• Exceptional Links and Twisted Fermi Ribbons in non-Hermitian Systems
• Non-Hermitean Localization and De-Localization
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• PT-Symmetric Plasmonic Metamaterials
• Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
• Topological phases and edge states in a non-Hermitian trimerized optical lattice
• Topological non-Hermitian origin of surface Maxwell waves
• Dynamical classification of topological quantum phases
• Topological Semimetals carrying Arbitrary Hopf Numbers: Hopf-Link, Solomon's-Knot, Trefoil-Knot and Other Semimetals
• Dynamical quantum phase transitions in non-Hermitian lattices
• Topological phase in a non-Hermitian PT symmetric system
• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
• Relation between $\mathcal{P}\mathcal{T}$-symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models
• Hall Conductance of a Non-Hermitian Chern Insulator
• Topological classification of non-Hermitian systems with reflection symmetry
• Breathers in PT-symmetric optical couplers
• Dissipative preparation of Chern insulators
• Topological quantum wires with balanced gain and loss
• Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov-de Gennes equation
• Time Dependent $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Pseudo-Hermiticity for a Class of Nondiagonalizable Hamiltonians
• Edge states at the interface of non-Hermitian systems
• Exceptional points in topological edge spectrum of PT symmetric domain walls
• Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model
• Weyl-link semimetals
• Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals
• PT Symmetric Aubry-Andre Model
• The C Operator in PT-Symmetric Quantum Theories
• Time-Reversal Symmetry in Non-Hermitian Systems
• Su-Schrieffer-Heeger chain with one pair of PT-symmetric defects
• Majorana Edge Modes with Gain and Loss
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• Topological phases in Kitaev chain with imbalanced pairing
• Theory of superconductivity with non-Hermitian and parity-time reversal symmetric cooper pairing symmetry
• Topological protection from exceptional points in Weyl and nodal line semimetals
• Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator
• Geometric Phase in PT-Symmetric Quantum Mechanics
• Hopf-link multi-Weyl-loop topological semimetals
• PT Symmetric Floquet Topological Phase
• Engineering three-dimensional topological insulators in Rashba-type spin-orbit coupled heterostructures
• Topological phonon polaritons in one-dimensional non-Hermitian nanoparticle chains
• Topological photonic states in one-dimensional dimerized ultracold atomic chains
• On the invariant method for the time-dependent non-Hermitian Hamiltonians
• Weyl semimetals and superconductors designed in an orbital selective superlattice
• Topological plasmons in dimerized chains of nanoparticles: robustness against long-range quasistatic interactions and retardation effects
• Non-Hermitian bidirectional robust transport
• PT Symmetric Floquet Topological Phase in SSH Model
• Wave scattering on a domain wall in a chain of PT-symmetric couplers
• Partial topological Zak phase and dynamical confinement in non-Hermitian bipartite system
• Double helix nodal line superconductor
• Dynamical topological invariant for non-Hermitian Rice-Mele model
• Erratum: Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians [J. Math. Phys. 43, 6343 (2002); math-ph/0207009]
• Time Reversal and Exceptional Points
• Topological Protection of Coherence in a Dissipative Environment
• Long-range entangled zero-mode state in a non-Hermitian lattice
• Exceptional points in quantum and classical dynamics
• Geometric phase and phase diagram for non-Hermitian quantum XY model
• Exceptional point description of one-dimensional chiral topological superconductors/superfluids in BDI class
• Chern number in Ising models with spatially modulated real and complex fields
• Cryptoreality of nonanticommutative Hamiltonians
• A black potential for spin less particles
• Pseudo topological insulators
• Photo-induced SU(3) topological material of spinless fermions
• The effects of dissipation on topological mechanical systems

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• Non-Hermitian topological phenomena: A review
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• Topological framework for directional amplification in driven-dissipative cavity arrays
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• Non-Hermitian route to higher-order topology in an acoustic crystal
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• Simulating non-Hermitian quasicrystals with single-photon quantum walks
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