Non-Hermitian Floquet Topological Matter -- A Review
arXiv:2305.16153 · doi:10.3390/e25101401
Abstract
The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matters due to their exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matters in one and two spatial dimensions. We first give a bird's-eye view of the literature for clarifying the physical significance of non-Hermitian Floquet systems. We then introduce, in a pedagogical manner, a number of useful tools tailored for the study of non-Hermitian Floquet systems and their topological properties. With the aid of these tools, we present typical examples of non-Hermitian Floquet topological insulators, superconductors, and quasicrystals, with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties, and localization transitions. We conclude this review by summarizing our main findings and presenting our vision of future directions.
arXiv comment86 pages, 10 figures, submitted
References in corpus (237)
- Photonic Floquet Topological Insulators
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Experimental realisation of the topological Haldane model
- Edge states and topological invariants of non-Hermitian systems
- Complex Extension of Quantum Mechanics
- Floquet Topological Insulator in Semiconductor Quantum Wells
- Exceptional Topology of Non-Hermitian Systems
- Non-Hermitian Physics
- Localization transitions in non-Hermitian quantum mechanics
- Topological phases of non-Hermitian systems
- The physics of exceptional points
- Photovoltaic Hall effect in graphene
- Symmetry and Topology in Non-Hermitian Physics
- Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
- Topological Origin of Non-Hermitian Skin Effects
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- 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
- Nonlinear waves in -symmetric systems
- Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
- Anomalous edge state in a non-Hermitian lattice
- Non-Bloch Band Theory of Non-Hermitian Systems
- Floquet Engineering of Quantum Materials
- Topological energy transfer in an optomechanical system with exceptional points
- Floquet Time Crystals
- Correspondence between winding numbers and skin modes in non-hermitian systems
- On the phase structure of driven quantum systems
- Observation of bulk boundary correspondence breakdown in topolectrical circuits
- Stimulated Raman adiabatic passage in physics, chemistry and beyond
- Non-Hermitian Boundary Modes
- Light-induced anomalous Hall effect in graphene
- Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
- 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
- Driven quantum transport on the nanoscale
- Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
- High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
- Non-Hermitian skin effect and chiral damping in open quantum systems
- Observation of topologically protected bound states in a one dimensional photonic system
- Discrete time crystals: rigidity, criticality, and realizations
- Non-Hermitian Topology and Exceptional-Point Geometries
- Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
- Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
- Observation of photonic anomalous Floquet Topological Insulators
- Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Nonthermal pathways to ultrafast control in quantum materials
- Biorthogonal Quantum Mechanics
- Floquet topological insulators
- Hybrid higher-order skin-topological modes in non-reciprocal systems
- Time crystals: a review
- Topological Transition in a Non-Hermitian Quantum Walk
- Non-Hermitian Topological Invariants in Real Space
- Topological phase transition in non-Hermitian quasicrystals
- Observation of parity-time symmetry breaking in a single spin system
- Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
- Universal non-Hermitian skin effect in two and higher dimensions
- 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
- Observation of the topological Anderson insulator in disordered atomic wires
- Nonlinear switching and solitons in PT-symmetric photonic systems
- Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
- Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators
- Periodic Table for Floquet Topological Insulators
- New topological invariants in non-Hermitian systems
- Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
- Observation of higher-order non-Hermitian skin effect
- Realization of an anomalous Floquet topological system with ultracold atoms
- Non-Hermitian Ring Laser Gyroscopes with Enhanced Sagnac Sensitivity
- Topological singularities and the general classification of Floquet-Bloch systems
- Topological Non-Hermitian skin effect
- Non-Hermitian Many-Body Localization
- Light-induced emergent phenomena in 2D materials and topological materials
- Parity-time-symmetric quantum critical phenomena
- Nonlinear control of PT-symmetry and non-Hermitian topological states
- Topological states of non-Hermitian systems
- Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
- Effective Hamiltonians for periodically driven systems
- Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
- Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
- Floquet engineering with quasienergy bands of periodically driven optical lattices
- Classification of Interacting Topological Floquet Phases in One Dimension
- Topology and Broken Symmetry in Floquet Systems
- Pseudospin-selective Floquet band engineering in black phosphorus
- Strongly-Correlated Electron-Photon Systems
- Observation of non-Bloch parity-time symmetry and exceptional points
- Detecting topological invariants in nonunitary discrete-time quantum walks
- Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
- Non-Hermitian systems and topology: A transfer-matrix perspective
- Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
- Thouless pumping and topology
- Tailoring quantum gases by Floquet engineering
- Topological Phases in Non-Hermitian Aubry-André-Harper Models
- Generating Many Majorana Modes via Periodic Driving: A Superconductor Model
- Non-Reciprocal gain in non-Hermitian time-Floquet Systems
- Non-Hermitian Kondo effect in ultracold alkaline-earth atoms
- Eigenvector statistics in non-Hermitian random matrix ensembles
- Observation of anomalous π modes in photonic Floquet engineering
- Topological Classification of Non-Hermitian Hamiltonians
- Distribution of Eigenvalues in Non-Hermitian Anderson Model
- Topological characterization of chiral models through their long time dynamics
- Measuring quantized circular dichroism in ultracold topological matter
- Non-Hermitean Localization and De-Localization
- Observation of non-Hermitian topological Anderson insulator in quantum dynamics
- Transient non-Hermitian skin effect
- Simulating non-Hermitian quasicrystals with single-photon quantum walks
- Dynamical classification of topological quantum phases
- Dynamical quantum phase transitions in non-Hermitian lattices
- Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry
- Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
- Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials
- Beyond the Quantum Adiabatic Approximation: Adiabatic Perturbation Theory
- Coupled-wire construction of static and Floquet second-order topological insulators
- Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
- Topological tight-binding models from non-trivial square roots
- Experimental realization of Floquet PT-symmetric systems
- Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
- Nonunitary Scaling Theory of Non-Hermitian Localization
- Quantized Adiabatic Transport in Momentum Space
- Floquet Topological Phases of Non-Hermitian Systems
- Topological classification of non-Hermitian systems with reflection symmetry
- Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
- Realization of the square-root higher-order topological insulator in electric circuits
- Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential
- Observation of Chiral State Transfer Without Encircling an Exceptional Point
- Floquet States in Open Quantum Systems
- Many-body topology of non-Hermitian systems
- Floquet dynamical quantum phase transitions
- Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics
- Hybrid skin-topological modes without asymmetric couplings
- Simulation of non-Abelian braiding in Majorana time crystals
- Counter-propagating edge modes and topological phases of a kicked quantum Hall system
- Symmetry breaking and spectral structure of the interacting Hatano-Nelson model
- Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
- AIII and BDI Topological Systems at Strong Disorder
- Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
- Non-Hermitian Skin Effects in Hermitian Correlated/Disordered Systems: Boundary-Sensitive/Insensitive Quantities and Pseudo Quantum Number
- Non-Hermitian fractional quantum Hall states
- Topological Effects in Chiral Symmetric Driven Systems
- Towards large-Chern-number topological phases by periodic quenching
- Realization of Anomalous Floquet Insulators in Strongly-Coupled Nanophotonic Lattices
- Square-root higher-order topological insulator on a decorated honeycomb lattice
- Non-Hermitian Many-Body Localization with Open Boundaries
- Acoustic square-root topological insulators
- Perspective: non-Hermitian physics in magnetic systems
- Photonic Floquet media with a complex time-periodic permittivity
- Floquet topological phases in a spin-1/2 double kicked rotor
- Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
- Topological phases and nonreciprocal edge states in non-Hermitian Floquet Insulators
- Measurement-only quantum computation with Majorana corner modes
- Exceptional Spin Liquids from Couplings to the Environment
- Anomalous Floquet non-Hermitian skin effect in a ring resonator lattice
- Recipe for creating an arbitrary number of Floquet chiral edge states
- Quantum computation via Floquet topological edge modes
- Stabilizing Non-Hermitian Systems by Periodic Driving
- Non-Hermitian Topological Phases: Principles and Prospects
- Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System
- Quantum and classical Floquet prethermalization
- Observation of pi/2 modes in an acoustic Floquet system
- Dynamical characterization of non-Hermitian Floquet topological phases in one-dimension
- Floquet Semimetal with Floquet-band Holonomy
- Tuning anomalous Floquet topological bands with ultracold atoms
- Floquet second-order topological insulators in non-Hermitian systems
- One-dimensional -root topological insulators and superconductors
- Analytic approaches to periodically driven closed quantum systems: Methods and Applications
- PT Symmetric Floquet Topological Phase
- Eigenvalue topology of non-Hermitian band structures in two and three dimensions
- Detecting topological invariants in chiral symmetric insulators via losses
- Dynamical signatures of topological order in the driven-dissipative Kitaev chain
- Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
- Condensed Matter Physics in Time Crystals
- Non-Hermitian Boundary State Engineering in Anomalous Floquet Topological Insulators
- Dual topological characterization of non-Hermitian Floquet phases
- Non-Hermitian Floquet topological phases in the double-kicked rotor
- Interaction-induced non-Hermitian topological phases from a dynamical gauge field
- Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice
- Exceptional points and the topology of quantum many-body spectra
- Systematic construction of square-root topological insulators and superconductors
- 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
- Dynamic winding number for exploring band topology
- Exceptional band touching for strongly correlated systems in equilibrium
- Non-Hermitian topological phases and dynamical quantum phase transitions: A generic connection
- Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model
- Time-dependent -symmetric quantum mechanics in generic non-Hermitian systems
- Non-Bloch band theory and bulk-edge correspondence in non-Hermitian systems
- Floquet exceptional points and chirality in non-Hermitian Hamiltonians
- Non-Hermitian spectra and Anderson localization
- -root weak, Chern, and higher-order topological insulators, and -root topological semimetals
- PT Symmetric Floquet Topological Phase in SSH Model
- Loss-induced Floquet non-Hermitian skin effect
- Symmetry and topological classification of Floquet non-Hermitian systems
- Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
- Engineering Floquet Dynamical Quantum Phase Transition
- Planck's quantum-driven integer quantum Hall effect in chaos
- From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
- Topological origin of quantized transport in non-Hermitian Floquet chains
- Observation of slowly decaying eigenmodes without exceptional points in Floquet, dissipative, synthetic circuits
- -symmetric, non-Hermitian quantum many-body physics -- a methodological perspective
- Driving-induced multiple -symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
- Square-root topological phase with time-reversal and particle-hole symmetry
- Topological swing in Bloch oscillations
- Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity
- Statistical Mechanics of Floquet Quantum Matter: Exact and Emergent Conservation Laws
- Non-Hermitian quasicrystal in dimerized lattices
- Topological properties of Floquet winding bands in a photonic lattice
- Driven quantum many-body systems and out-of-equilibrium topology
- Controlling Exceptional Points with Light
- Floquet engineering and simulating exceptional rings with a quantum spin system
- Square-root Floquet topological phases and time crystals
- Directed momentum current induced by the PT-symmetric driving
- Observation of Floquet topological phases with large Chern numbers
- Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
- Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
- Floquet dynamical quantum phase transitions in periodically quenched systems
- Light-driven Lifshitz transitions in non-Hermitian multi-Weyl semimetals
- Non-Hermitian Weyl semimetal and its Floquet engineering
- Emergence of integer quantum Hall effect from chaos
- Persistence of Topological Phases in Non-Hermitian Quantum Walks
- Super-exponential scrambling of Out-of-time-ordered correlators
- Realizing Topological Transition in a Non-Hermitian Quantum Walk with Circuit QED
- Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
- Hexagonally warped exceptional physics in multi-Weyl semimetals
- Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence
- Super-exponential diffusion in nonlinear non-Hermitian systems
- Emergent conservation in Floquet dynamics of integrable non-Hermitian models
- Entanglement spectrum and entropy in Floquet topological matter
- Non-Hermitian Avalanche Effect: Non-Perturbative Effect Induced by Local Non-Hermitian Perturbation on a Z2 Topological Order
- Unravelling the edge spectra of non-Hermitian Chern insulators
- Connecting active and passive -symmetric Floquet modulation models
- Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
- Anomalous second-order skin modes in Floquet non-Hermitian systems
- Topological modes and beyond
- Floquet States
Cited by in corpus (30)
- Floquet engineering of point-gapped topological superconductors
- Emergent entanglement phase transitions in non-Hermitian Aubry-André-Harper chains
- Ring Structure in the Complex Plane: A Fingerprint of non-Hermitian Mobility Edge
- Entanglement phase transitions in non-Hermitian quasicrystals
- Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
- A brief review of hybrid skin-topological effect
- Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
- The non-Hermitian skin effect: A perspective
- Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
- Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence
- Entanglement phase transitions in non-Hermitian Floquet systems
- Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
- Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
- Biorthogonal topological charge pumping in non-Hermitian systems
- Gapless higher-order topology and corner states in Floquet systems
- Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
- Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems
- Entanglement phase transitions in non-Hermitian Kitaev chains
- Floquet non-Abelian topological charges and edge states
- Retrieving maximum information of symmetric states from their corrupted copies
- Quantum geometry and geometric entanglement entropy of one-dimensional Floquet topological matter
- Floquet Möbius topological insulators
- Exceptional points in SSH-like models with hopping amplitude gradient
- Tailoring higher-order van Hove singularities in non-Hermitian interface systems via Floquet engineering
- Superiority of Krylov shadow tomography in estimating quantum Fisher information: From bounds to exactness
- Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
- Topology and edge modes surviving criticality in non-Hermitian Floquet systems
- Coupled-wire construction of non-Abelian higher-order topological phases
- Non-Hermitian Floquet dynamics in absorption spectroscopy
- Liouvillian topology and nonreciprocal dynamics in open Floquet chains