Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point

Abstract

The discovery of novel topological phase advances our knowledge of nature and stimulates the development of applications. In non-Hermitian topological systems, the topology of band touching exceptional points is very important. Here we propose a real-energy topological gapless phase arising from exceptional points in one dimension, which has identical topological invariants as the topological gapless phase arising from degeneracy points. We develop a graphic approach to characterize the topological phases, where the eigenstates of energy bands are mapped to the graphs on a torus. The topologies of different phases are visualized and distinguishable; and the topological gapless edge state with amplification appropriate for topological lasing exists in the nontrivial phase. These results are elucidated through a non-Hermitian Su-Schrieffer-Heeger ladder. Our findings open new way for identifying topology phase of matter from visualizing the eigenstates.

10 pages, 3 figures + 2 pages, 1 figure

References in corpus (168)

• The electronic properties of graphene
• Topological Insulators
• Topological insulators and superconductors
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Topological Photonics
• Topological Photonics
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Photonic Floquet Topological Insulators
• Helical liquids and Majorana bound states in quantum wires
• Making Sense of Non-Hermitian Hamiltonians
• Classification of topological quantum matter with symmetries
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Weyl Semimetal in a Topological Insulator Multilayer
• Edge states and topological invariants of non-Hermitian systems
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Dirac semimetal in three dimensions
• Imaging topological edge states in silicon photonics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class
• Robust optical delay lines via topological protection
• Topological phases of non-Hermitian systems
• Observation of a topological 3D Dirac semimetal phase in high-mobility Cd3As2
• Symmetry and Topology in Non-Hermitian Physics
• Topological Acoustics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Acoustic topological insulator and robust one-way sound transport
• Topological Band Theory for Non-Hermitian Hamiltonians
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Experimental observation of Weyl points
• Observation of Weyl nodes in TaAs
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Topological energy transfer in an optomechanical system with exceptional points
• Lasing in topological edge states of a 1D lattice
• Topological Bands for Ultracold Atoms
• Visualization of Branch Points in PT-Symmetric Waveguides
• Non-Hermitian Chern bands
• Quantum Hall effects in a Weyl Semi-Metal: possible application in pyrochlore Iridates
• Spawning rings of exceptional points out of Dirac cones
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Topolectrical circuits
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Floquet Topological Insulators for Sound
• Non-Hermitian skin effect and chiral damping in open quantum systems
• The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi
• Exciton-polariton topological insulator
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
• Topology by Dissipation in Atomic Quantum Wires
• Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Quantum anomalous Hall effect and related topological electronic states
• Edge states and topological phases in non-Hermitian systems
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Topological phase transition in non-Hermitian quasicrystals
• Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Topological Hybrid Silicon Microlasers
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Synthetic gauge fields and Weyl point in Time-Reversal Invariant Acoustic Systems
• Topologically protected midgap states in complex photonic lattices
• Topological and magnetic phases of interacting electrons in the pyrochlore iridates
• 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
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• Edge Solitons in Nonlinear Photonic Topological Insulators
• New topological invariants in non-Hermitian systems
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Optical Resonator Analog of a Two-Dimensional Topological Insulator
• Experimental realization of a Weyl exceptional ring
• A topological source of quantum light
• Experimental observation of optical Weyl points
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Higher-order topological corner states induced by gain and loss
• Topologically Robust Transport of Photons in a Synthetic Gauge Field
• Topological states of non-Hermitian systems
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Encircling an Exceptional Point
• Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Topological invariance and global Berry phase in non-Hermitian systems
• Symmetry-protected nodal phases in non-Hermitian systems
• Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Simultaneous Observation of Topological Edge State and Exceptional Point in an Open and Non-Hermitian System
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Topological semimetal in a fermionic optical lattice
• Measurement of topological invariants in a 2D photonic system
• Anomalous helical edge states in a non-Hermitian Chern insulator
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point
• Bulk Dirac points in distorted spinels
• Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
• Parity-time-symmetric topological superconductor
• Exceptional Links and Twisted Fermi Ribbons in non-Hermitian Systems
• Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
• Topological phases and edge states in a non-Hermitian trimerized optical lattice
• Edge states in trimer lattices
• Knotted Non-Hermitian Metals
• Topological phase in a non-Hermitian PT symmetric system
• Dynamical quantum phase transitions in non-Hermitian lattices
• Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
• Hall Conductance of a Non-Hermitian Chern Insulator
• Experimental demonstration of an anisotropic exceptional point
• Constant-intensity waves and their modulation instability in non-Hermitian potentials
• Topological classification of non-Hermitian systems with reflection symmetry
• Topological quantum wires with balanced gain and loss
• Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov-de Gennes equation
• Exceptional Points in a Non-Hermitian Topological Pump
• Bulk-boundary correspondence for non-Hermitian Hamiltonians via Green functions
• Edge states at the interface of non-Hermitian systems
• Exceptional points in topological edge spectrum of PT symmetric domain walls
• Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals
• Geometric classification of non-Hermitian topological systems through the singularity ring
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Electric circuits for non-Hermitian Chern insulators
• 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
• Topological band theory for non-Hermitian systems from the Dirac equation
• Theory of superconductivity with non-Hermitian and parity-time reversal symmetric cooper pairing symmetry
• Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator
• Topological nodal points in two coupled SSH chains
• Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice
• Topological protection from exceptional points in Weyl and nodal line semimetals
• Effects of Non-Hermiticity on Su-Schrieffer-Heeger Defect States
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Topological bands and triply-degenerate points in non-Hermitian hyperbolic metamaterials
• Symmetry protected topological phases characterized by isolated exceptional points
• Detecting topological invariants in chiral symmetric insulators via losses
• Topological photonic states in one-dimensional dimerized ultracold atomic chains
• Topological phonon polaritons in one-dimensional non-Hermitian nanoparticle chains
• Topological Phase Transition Independent of System Non-Hermiticity
• Topology and Observables of the Non-Hermitian Chern Insulator
• Topological multiband photonic superlattices
• Topology and exceptional points of massive Dirac models with generic non-Hermitian perturbations
• Bulk and edge-state arcs in non-hermitian coupled-resonator arrays
• Theory of chiral edge state lasing in a two-dimensional topological system
• Stable topological edge states in a non-Hermitian four-band model
• Inversion symmetric non-Hermitian Chern insulator
• Partial topological Zak phase and dynamical confinement in non-Hermitian bipartite system
• Dynamical topological invariant for non-Hermitian Rice-Mele model
• Nodal Manifolds Bounded by Exceptional Points on Non-Hermitian Honeycomb Lattices and Electrical-Circuit Realizations
• Extended Bloch theorem for topological lattice models with open boundaries
• Complex magnetic monopoles, geometric phases and quantum evolution in vicinity of diabolic and exceptional points
• Generalized Berry phase for a bosonic Bogoliubov system with exceptional points
• Survival, decay, and topological protection in non-Hermitian quantum transport
• Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system
• PC-symmetry-protected edge states in interacting driven-dissipative bosonic systems
• Non-Hermitian Photonics based on Charge-Parity Symmetry

Cited by in corpus (5)

• Knots and Non-Hermitian Bloch Bands
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Berry curvature inside parity-time-symmetry protected exceptional surface