Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems

Abstract

We present a pedagogical review of the periodically driven non-Hermitian systems, particularly on the rich interplay between the non-Hermitian skin effect and the topology. We start by reviewing the non-Bloch band theory of the static non-Hermitian systems and discuss the establishment of its generalized bulk-boundary correspondence. Ultimately, we focus on the non-Bloch band theory of two typical periodically driven non-Hermitian systems: harmonically driven non-Hermitian system and periodically quenched non-Hermitian system. The non-Bloch topological invariants were defined on the generalized Brillouin zone and the real space wave functions to characterize the Floquet non-Hermtian topological phases. Then, the generalized bulk-boundary correspondence was established for the two typical periodically driven non-Hermitian systems. Additionally, we review novel phenomena in the higher-dimensional periodically driven non-Hermitian systems, including Floquet non-Hermitian higher-order topological phases and Floquet hybrid skin-topological modes. The experimental realizations and recent advances have also been surveyed. Finally, we end with a summarization and hope this pedagogical review can motivate further research on Floquet non-Hermtian topological physics.

arXiv comment29 pages,16 figures, Topical Review

References in corpus (188)

• 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
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Photonic Floquet Topological Insulators
• Making Sense of Non-Hermitian Hamiltonians
• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• Topological invariants of time-reversal-invariant band structures
• Experimental realisation of the topological Haldane model
• Edge states and topological invariants of non-Hermitian systems
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Search for Majorana fermions in superconductors
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Non-Hermitian Physics
• Higher-Order Topological Insulators
• Colloquium: Topological Band Theory
• Robust optical delay lines via topological protection
• Topological phases of non-Hermitian systems
• Photovoltaic Hall effect in graphene
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Observation of Floquet-Bloch states on the surface of a topological insulator
• Atomic quantum gases in periodically driven optical lattices
• Topological Band Theory for Non-Hermitian Hamiltonians
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Floquet Engineering of Quantum Materials
• Topological Bands for Ultracold Atoms
• Non-Hermitian Chern bands
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Non-Hermitian Boundary Modes
• Spawning rings of exceptional points out of Dirac cones
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Anatomy of skin modes and topology in non-Hermitian systems
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Topological Thouless Pumping of Ultracold Fermions
• Floquet Topological Insulators for Sound
• Non-Hermitian Topology and Exceptional-Point Geometries
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Topology by Dissipation in Atomic Quantum Wires
• Observation of photonic anomalous Floquet Topological Insulators
• Classical higher-order topological insulators
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Non-Hermitian Topological Invariants in Real Space
• Topologically protected acoustic helical edge states and interface states in strongly coupled metamaterial ring lattices
• Topological phase transition in non-Hermitian quasicrystals
• Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
• Universal non-Hermitian skin effect in two and higher dimensions
• Reciprocal skin effect and its realization in a topolectrical circuit
• Selective scattering between Floquet-Bloch and Volkov states in a topological insulator
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Non-Hermitian topological phenomena: A review
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Higher-order non-Hermitian skin effect
• Acoustic non-Hermitian skin effect from twisted winding topology
• Observation of higher-order non-Hermitian skin effect
• Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
• Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
• Topological Non-Hermitian skin effect
• PT-Symmetric Electronics
• Nonlinear control of PT-symmetry and non-Hermitian topological states
• Higher-order topological corner states induced by gain and loss
• 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
• Non-Hermitian Morphing of Topological Modes
• Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• 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
• Transport signatures of Floquet Majorana fermions in driven topological superconductors
• Observation of non-Bloch parity-time symmetry and exceptional points
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Heralded magnetism in non-Hermitian atomic systems
• Topological Phases in Non-Hermitian Aubry-André-Harper Models
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Non-Reciprocal gain in non-Hermitian time-Floquet Systems
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Observation of anomalous π modes in photonic Floquet engineering
• Non-Hermitian route to higher-order topology in an acoustic crystal
• Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
• Gain and loss induced topological insulating phase in a non Hermitian electrical circuit
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Exceptional Links and Twisted Fermi Ribbons in non-Hermitian Systems
• Synthetic Gauge Fields for Vibrational Excitations of Trapped ions
• Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
• Staggered-Vortex Superfluid of Ultracold Bosons in an Optical Lattice
• Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Non-Hermitian Linear Response Theory
• Measurement of a topological edge invariant in a microwave network
• Hall Conductance of a Non-Hermitian Chern Insulator
• Non-Hermitian Dirac Cones
• Experimental realization of Floquet PT-symmetric systems
• Floquet Topological Phases of Non-Hermitian Systems
• Quantized Adiabatic Transport in Momentum Space
• Mirror skin effect and its electric circuit simulation
• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Non-Hermitian second-order skin and topological modes
• Exceptional rings protected by emergent symmetry for mechanical systems
• Bypassing the bandwidth theorem with PT symmetry
• Topological quantum wires with balanced gain and loss
• Second-order Topological Superconductors with Mixed Pairing
• Anderson localization in the Non-Hermitian Aubry-André-Harper model with physical gain and loss
• Jones polynomial and knot transitions in topological semimetals
• Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics
• Hybrid skin-topological modes without asymmetric couplings
• Complex classes of periodically driven topological lattice systems
• Defective Edge States and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Observation of non-Hermitian topology with non-unitary dynamics of solid-state spins
• Photonic Floquet media with a complex time-periodic permittivity
• Floquet Chern Insulators of Light
• Floquet topological phases in a spin-1/2 double kicked rotor
• Experimental identification of the second-order non-Hermitian skin effect with physics-graph-informed machine learning
• Anomalous Floquet non-Hermitian skin effect in a ring resonator lattice
• Topological phases and nonreciprocal edge states in non-Hermitian Floquet Insulators
• Exceptional Spin Liquids from Couplings to the Environment
• Non-Bloch $\mathcal{P}\mathcal{T}$ symmetry breaking in non-Hermitian Photonic Quantum Walks
• Non-Hermitian Topological Phases: Principles and Prospects
• Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Observation of pi/2 modes in an acoustic Floquet system
• Dynamical characterization of non-Hermitian Floquet topological phases in one-dimension
• Floquet second-order topological insulators in non-Hermitian systems
• Non-Hermitian Boundary State Engineering in Anomalous Floquet Topological Insulators
• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Floquet Mechanism for Non-Abelian Fractional Quantum Hall States
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Dual topological characterization of non-Hermitian Floquet phases
• Non-Hermitian Floquet Topological Matter -- A Review
• Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Floquet exceptional points and chirality in non-Hermitian Hamiltonians
• Universal fluctuations of Floquet topological invariants at low frequencies
• State-recycling and time-resolved imaging in topological photonic lattices
• Floquet engineering of optical solenoids and quantized charge pumping along tailored paths in two-dimensional Chern insulators
• Non-Hermitian Majorana modes protect degenerate steady states
• PT Symmetric Floquet Topological Phase in SSH Model
• Loss-induced Floquet non-Hermitian skin effect
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• 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
• Topological origin of quantized transport in non-Hermitian Floquet chains
• Observation of slowly decaying eigenmodes without exceptional points in Floquet, dissipative, synthetic circuits
• Driving-induced multiple $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
• Topological properties of Floquet winding bands in a photonic lattice
• Controlling Exceptional Points with Light
• Floquet engineering and simulating exceptional rings with a quantum spin system
• Directed momentum current induced by the PT-symmetric driving
• Non-Hermitian Weyl semimetal and its Floquet engineering
• Light-driven Lifshitz transitions in non-Hermitian multi-Weyl semimetals
• Degeneracy and defectiveness in non-Hermitian systems with open boundary
• Persistence of Topological Phases in Non-Hermitian Quantum Walks
• Non-Hermitian impurities in Dirac systems
• Super-exponential scrambling of Out-of-time-ordered correlators
• Realizing Topological Transition in a Non-Hermitian Quantum Walk with Circuit QED
• Generalized Bloch band theory for non-Hermitian bulk-boundary correspondence
• Hexagonally warped exceptional physics in multi-Weyl semimetals
• Evidencing non-Bloch dynamics in temporal topolectrical circuits
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Universal characteristics of one-dimensional non-Hermitian superconductors
• Anomalous second-order skin modes in Floquet non-Hermitian systems
• Non-Floquet engineering in periodically driven non-Hermitian systems
• Wannier-Stark localization in one-dimensional amplitude-chirped lattices

Cited by in corpus (9)

• Floquet engineering of point-gapped topological superconductors
• Non-Hermitian Second-Order Topological Phases and Bipolar Skin Effect in Photonic Kagome Crystals
• Anomalous pumping in the non-Hermitian Rice-Mele model
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Non-Hermitian higher-order topological insulators enabled by altermagnet engineering
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal