Symmetry protected topological phases characterized by isolated exceptional points

Abstract

Exceptional point (EP) associated with eigenstates coalescence in non-Hermitian systems has many exotic features. The EPs are generally sensitive to system parameters, here we report symmetry protected isolated EPs in the Brillouin zone (BZ) of a two-dimensional non-Hermitian bilayer square lattice; protected by symmetry, the isolated EPs only move, merge, and split in the BZ. The average values of Pauli matrices under the eigenstate of system Bloch Hamiltonian define a real planar vector field, the topological defects of which are isolated EPs associated with vortices. The winding number characterizes the vortices and reveals the topological properties of the non- Hermitian system. Different topological phases correspond to different EP configurations, which are unchanged unless topological phase transition occurs accompanying with the EPs merging or splitting.

References in corpus (118)

• Many-Body Physics with Ultracold Gases
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Insulators with Inversion Symmetry
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Making Sense of Non-Hermitian Hamiltonians
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Weyl Semimetal in a Topological Insulator Multilayer
• Edge states and topological invariants of non-Hermitian systems
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Dirac semimetal in three dimensions
• Experimental discovery of Weyl semimetal TaAs
• Three Dimensional Dirac Semimetal and Quantum Transports in Cd3As2
• Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class
• Robust optical delay lines via topological protection
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• Topological Crystalline Insulators in the SnTe Material Class
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Observation of a topological 3D Dirac semimetal phase in high-mobility Cd3As2
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• 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
• Anomalous edge state in a non-Hermitian lattice
• Observation of Weyl nodes in TaAs
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Topological energy transfer in an optomechanical system with exceptional points
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Observation of tunable bandgap and anisotropic Dirac semimetal state in black phosphorus
• Lasing in topological edge states of a 1D lattice
• 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
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Condensed Matter Theory of Dipolar Quantum Gases
• Synthetic three-dimensional atomic structures assembled atom by atom
• 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
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Edge states and topological phases in non-Hermitian systems
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Topological Hybrid Silicon Microlasers
• 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
• 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
• Time-reversal invariant realization of the Weyl semimetal phase
• Merging of Dirac points in a two-dimensional crystal
• Experimental Observation of Large Chern numbers in Photonic Crystals
• Optical Resonator Analog of a Two-Dimensional Topological Insulator
• Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices
• Dynamically encircling exceptional points: Exact evolution and polarization state conversion
• Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
• Dirac and Weyl Superconductors in Three Dimensions
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• PT-symmetry in honeycomb photonic lattices
• Topology by dissipation
• 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
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• A new magnetic field dependence of Landau levels on a graphene like structure
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Topological invariance and global Berry phase in non-Hermitian systems
• Symmetry-protected nodal phases in non-Hermitian systems
• Realization of 2D Spin-orbit Interaction and Exotic Topological Orders in Cold Atoms
• 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
• Tight-binding modeling and low-energy behavior of the semi-Dirac point
• The Chirality of Exceptional Points
• Observation of a Chiral State in a Microwave Cavity
• Coexistence of quantized and non-quantized geometric phases in quasi-one-dimensional systems without inversion symmetry
• Topological semimetal in a fermionic optical lattice
• Measurement of topological invariants in a 2D photonic system
• Geometric phase around exceptional points
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Coalescence of spectral singularities and phase diagrams for one-dimensional PT symmetric photonic crystals
• 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
• Topological phase in a non-Hermitian PT symmetric system
• Exceptional contours and band structure design in parity-time symmetric photonic crystals
• Bloch-Zener oscillations across a merging transition of Dirac points
• Relation between $\mathcal{P}\mathcal{T}$-symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models
• Incident Direction Independent Wave Propagation and Unidirectional Lasing
• Dissipative preparation of Chern insulators
• Majorana Modes in Driven-Dissipative Atomic Superfluids With Zero Chern Number
• Detecting Topological Phases in Cold Atoms
• Su-Schrieffer-Heeger chain with one pair of PT-symmetric defects
• Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice
• Quantum simulation of exotic PT-invariant topological nodal loop bands with ultracold atoms in an optical lattice
• Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation
• Floquet band structure of a semi-Dirac system
• Parity-time symmetric coupled asymmetric dimers
• Quadratic band touching points and flat bands in two-dimensional topological Floquet systems
• Dirac and Weyl Rings in Three Dimensional Cold Atom Optical Lattices
• Long-range entangled zero-mode state in a non-Hermitian lattice
• Moving and merging of Dirac points on a square lattice and hidden symmetry protection
• Proximity effects in cold atom artificial graphene
• Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system

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• Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics
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• Two-dimensional non-Hermitian topological phases induced by asymmetric hopping in a one-dimensional superlattice
• State-dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems
• Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays
• Spectral and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric tight-binding chain with gain and loss
• Non-Hermitian semi-Dirac semi-metals
• Defective Edge states and Anomalous Bulk-boundary Correspondence for Topological Insulators under Non-Hermitian Similarity Transformation
• Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Topological Phase Transition of A Non-Hermitian Crosslinked Chain
• Semi-localization transition driven by a single asymmetrical tunneling
• Zero modes of velocity field and topological invariant in quantum torus
• Correspondence between non-Hermitian topology and directional amplification in the presence of disorder