Exceptional Topological Insulators

Abstract

We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding. We show how this phase can evolve from a Weyl semimetal or Hermitian three-dimensional topological insulator close to criticality when quasiparticles acquire a finite lifetime. The ETI does not require any symmetry to be stabilized. It is characterized by a bulk energy point gap, and exhibits robust surface states that cover the bulk gap as a single sheet of complex eigenvalues or with a single exceptional point. The ETI can be induced universally in gapless solid-state systems, thereby setting a paradigm for non-Hermitian topological matter.

arXiv comment6+ pages, 3 figures; 21 pages Supplemental Material

References in corpus (49)

• Topological Insulators
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Insulators in Three Dimensions
• Classification of topological insulators and superconductors in three spatial dimensions
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Topological invariants of time-reversal-invariant band structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Edge states and topological invariants of non-Hermitian systems
• First observation of Spin-Momentum Helical Locking in Bi2Se3 and Bi2Te3, demonstration of Topological-Order at 300K and a realization of topological-transport-regime
• Exceptional Topology of Non-Hermitian Systems
• Topological Materials: Weyl Semimetals
• Electron-phonon interactions from first principles
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Reflection symmetric second-order topological insulators and superconductors
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Non-Hermitian Boundary Modes
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Anatomy of skin modes and topology in non-Hermitian systems
• Topological Boundary Modes in Isostatic Lattices
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Topolectrical circuits
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Exceptional Points of Non-hermitian Operators
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Realization of a three-dimensional photonic topological insulator
• Higher-order non-Hermitian skin effect
• New topological invariants in non-Hermitian systems
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Boundary Green functions of topological insulators and superconductors
• Non-Hermitian topology: a unifying framework for the Andreev versus Majorana states controversy
• Fermion doubling theorems in 2D non-Hermitian systems for Fermi points and exceptional points
• Non-Hermitian Topological Theory of Finite-Lifetime Quasiparticles: Prediction of Bulk Fermi Arc Due to Exceptional Point
• Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime
• Quantitative reliability of Migdal-Eliashberg theory for strong electron-phonon coupling
• Topological Hopf-Chern Insulators and the Hopf Superconductor
• Topology and Observables of the Non-Hermitian Chern Insulator
• Floquet chiral magnetic effect
• Migdal's theorem and electron-phonon vertex corrections in Dirac materials
• Three-dimensional Chiral Lattice Fermion in Floquet Systems
• Dissipative analog of four-dimensional quantum Hall physics

Cited by in corpus (74)

• Non-Hermitian Topology and Exceptional-Point Geometries
• Universal non-Hermitian skin effect in two and higher dimensions
• Higher-order non-Hermitian skin effect
• Topological Non-Hermitian skin effect
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Non-Hermitian second-order skin and topological modes
• Many-body topology of non-Hermitian systems
• Symmetry breaking and spectral structure of the interacting Hatano-Nelson model
• Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
• Knot topology of exceptional point and non-Hermitian no-go theorem
• Dislocation Non-Hermitian Skin Effect
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Floquet engineering of point-gapped topological superconductors
• Non-Hermitian Mott Skin Effect
• Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems
• Hermitian Bulk -- Non-Hermitian Boundary Correspondence
• Zoology of non-Hermitian spectra and their graph topology
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Bulk-boundary correspondence in point-gap topological phases
• Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification
• Symmetry indicator in non-Hermitian systems
• 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
• Non-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals
• Degeneracy and defectiveness in non-Hermitian systems with open boundary
• Non-Hermitian Topology in Hermitian Topological Matter
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Non-Hermitian Dirac cones with valley-dependent lifetimes
• Hexagonally warped exceptional physics in multi-Weyl semimetals
• Exact formulas of the end-to-end Green's functions in non-Hermitian systems
• Non-Hermitian topology and criticality in photonic arrays with engineered losses
• Field theory of non-Hermitian disordered systems
• Topological superconductivity enhanced by exceptional points
• Chemical Principles of Intrinsic Topological Superconductors
• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Pseudospin-orbit coupling and non-Hermitian effects in the Quantum Geometric Tensor of a plasmonic lattice
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• Dynamical signatures of point-gap Weyl semimetal
• Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Nontrivial worldline winding in non-Hermitian quantum systems
• Floquet Exceptional Topological Insulator
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Multifractality of many-body non-Hermitian skin effect
• Constraints of internal symmetry on the non-Hermitian skin effect and bidirectional skin effect under the action of the Hermitian conjugate of time-reversal symmetry
• Topological Phases of Tight-Binding Trimer Lattice in the BDI Symmetry Class
• Anomalous second-order skin modes in Floquet non-Hermitian systems
• Surface exceptional points in a topological Kondo insulator
• Complex semiclassical theory for non-Hermitian quantum systems
• Magnetic Flux Response of Non-Hermitian Topological Phases
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Majorana zero-modes in a dissipative Rashba nanowire
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• General theory for infernal points in non-Hermitian systems
• Super-enhanced Sensitivity in Non-Hermitian Systems at Infernal Points
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Theory for the spectral splitting exponent of exceptional points
• $K$-theory classification of Wannier localizability and detachable topological boundary states
• Exceptional second-order topological insulators
• Topologically protected negative entanglement
• Hermitian and non-Hermitian topology in active matter
• Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system
• Fragmented exceptional points and their bulk and edge realizations in lattice models
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• Exceptional mode topological surface laser
• Non-Hermitian Hopf insulators
• Adiabatic charge transport through non-Bloch bands
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Intrinsic non-Hermitian topological phases
• Substrate Effect on Electronic Band Structure and Topological Property in Monolayer V2O3 Magnetic Topological Insulator
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension
• Continuum Landau surface states in a non-Hermitian Weyl semimetal