Topological States and Adiabatic Pumping in Quasicrystals

Abstract

The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i) quasicrystals exhibit nontrivial topological properties and (ii) these properties are attributed to dimensions higher than that of the quasicrystal. Specifically, we show, both theoretically and experimentally, that one-dimensional quasicrystals are assigned two-dimensional Chern numbers and, respectively, exhibit topologically protected boundary states equivalent to the edge states of a two-dimensional quantum Hall system.We harness the topological nature of these states to adiabatically pump light across the quasicrystal. We generalize our results to higher-dimensional systems and other topological indices. Hence, quasicrystals offer a new platform for the study of topological phases while their topology may better explain their surface properties.

10 pages, 5 figures, 4 appendices

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Cited by in corpus (625)

• Topological Photonics
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• Photonic Floquet Topological Insulators
• Classification of topological quantum matter with symmetries
• Non-Hermitian Physics
• Imaging topological edge states in silicon photonics
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• Anomalous edge state in a non-Hermitian lattice
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Topological Bands for Ultracold Atoms
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Topolectrical circuits
• Deterministic photon-emitter coupling in chiral photonic circuits
• Nonlinear topological photonics
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Photonic quadrupole topological phases
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Synthetic Dimension in Photonics
• Observation of the topological soliton state in the Su-Schrieffer-Heeger model
• Spectral signatures of many-body localization with interacting photons
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Topological phase transition in non-Hermitian quasicrystals
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Topologically protected midgap states in complex photonic lattices
• Topological quantum matter in synthetic dimensions
• Interacting topological insulators: a review
• Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Observation of the topological Anderson insulator in disordered atomic wires
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• Topological properties of linear circuit lattices
• Topology of photonic time-crystals
• Experimental Observation of Large Chern numbers in Photonic Crystals
• Experimental realization of a Weyl exceptional ring
• A topological source of quantum light
• Topological quantum matter with cold atoms
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Topological creation and destruction of edge states in photonic graphene
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
• Higher-order topological corner states induced by gain and loss
• Topologically Robust Transport of Photons in a Synthetic Gauge Field
• Topological phases of generalized Su-Schrieffer-Heeger models
• Robust light transport in non-Hermitian photonic lattices
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Higher-Order Topological Insulators in Quasicrystals
• Simultaneous Observation of Topological Edge State and Exceptional Point in an Open and Non-Hermitian System
• Topological Insulators in Random Lattices
• Experimental Measurement of the Berry Curvature from Anomalous Transport
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Thouless pumping and topology
• Quantized Nonlinear Thouless Pumping
• Measurement of topological invariants in a 2D photonic system
• Topological Phases in Non-Hermitian Aubry-André-Harper Models
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Matter-wave diffraction from a quasicrystalline optical lattice
• Observation of anomalous π modes in photonic Floquet engineering
• Quantum simulation of 2d topological physics using orbital-angular-momentum-carrying photons in a 1d array of cavities
• Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space
• Experimental band structure spectroscopy along a synthetic dimension
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Perspective on topological states of non-Hermitian lattices
• Edge states and topological pumping in elastic lattices with periodically modulated coupling
• Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators
• Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains
• Topological edge states in the one-dimensional super-lattice Bose-Hubbard model
• Topological phases without crystalline counterparts
• Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
• Topological light-trapping on a dislocation
• Quantum interference of topological states of light
• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Topological Phase Transitions and Thouless Pumping of Light in Photonic Waveguide Arrays
• Edge states in trimer lattices
• Topological phase in a non-Hermitian PT symmetric system
• Non-Hermitian Topological Anderson Insulators
• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• Measurement of the Zak phase of photonic bands through the interface states of metasurface/photonic crystal
• Experimental observation of temporal pumping in electro-mechanical waveguides
• Measurement of a topological edge invariant in a microwave network
• Experimental observation of non-reciprocal band-gaps in a space-time modulated beam using a shunted piezoelectric array
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal
• Quantized Fractional Thouless Pumping of Solitons
• Higher-order photonic topological states in surface-wave photonic crystals
• Exceptional Points in a Non-Hermitian Topological Pump
• Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices
• Observation of topological transport quantization by dissipation in fast Thouless pumps
• Nonlinear Thouless pumping: solitons and transport breakdown
• Observation of topological edge modes in a quasi-periodic acoustic waveguide
• Complex classes of periodically driven topological lattice systems
• Competition and interplay between topology and quasi-periodic disorder in Thouless pumping of ultracold atoms
• Measuring topological invariants in photonic systems
• Topological pumping of edge states via adiabatic passage
• Direct Observation of Topology from Single-photon Dynamics on a Photonic Chip
• Radiative topological states in resonant photonic crystals
• Experimental Observation of Nonreciprocal Waves in a Resonant Metamaterial Beam
• Experimental Demonstration of Dynamic Topological Pumping Across Incommensurate Bilayered Acoustic Metamaterials
• Amorphous photonic topological insulator
• Measuring topological invariants from generalized edge states in polaritonic quasicrystals
• Atom-optics simulator of lattice transport phenomena
• Localization transitions and mobility edges in coupled Aubry-André chains
• Rydberg-Atom Quantum Simulation and Chern Number Characterization of a Topological Mott Insulator
• Tutorial: synthetic frequency dimensions in dynamically modulated ring resonators
• The 6D quantum Hall effect and 3D topological pumps
• Topological Effects in Chiral Symmetric Driven Systems
• An atom optics approach to studying lattice transport phenomena
• Spin pumping and measurement of spin currents in optical superlattices
• Landau-Zener Transition in Topological Acoustic Pumping
• Edge States and Topological Pumping in Stiffness Modulated Elastic Plates
• Non-Abelian braiding of light
• Fast and robust quantum state transfer in a topological Su-Schrieffer-Heeger chain with Next-to-Nearest-Neighbour interactions
• Topological states on fractal lattices
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Topological lasing and self-induced transparency in two level systems
• Topological pumping of photons in nonlinear resonator arrays
• Anderson localization transitions with and without random potentials
• Topological equivalence of crystal and quasicrystal band structures
• Higher-Order topological insulator in a dodecagonal quasicrystal
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• Mode-Locked Topological Insulator Laser Utilizing Synthetic Dimensions
• Topological charge pumping in the interacting bosonic Rice-Mele model
• Anomalous transport in the Aubry-André-Harper model in isolated and open systems
• Topological insulator and particle pumping in a one-dimensional shaken optical lattice
• Dynamically manipulating topological physics and edge modes in a single degenerate optical cavity
• Tunable quantum interference using a topological source of indistinguishable photon pairs
• Mixed spectra and partially extended states in a two-dimensional quasiperiodic model
• Probing Weyl Physics with One-dimensional Sonic Crystals
• Revealing the topology of quasicrystals with a diffraction experiment
• Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices
• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
• Twisted quadrupole topological photonic crystals
• Robustness of topologically protected edge states in quantum walk experiments with neutral atoms
• Majorana fermions in density modulated p-wave superconducting wires
• Spectral imaging of topological edge states in plasmonic waveguide arrays
• The Aubry-André model as the hobbyhorse for understanding localization phenomenon
• Thermal Instability of Protected End States in a 1-D Topological Insulator
• Probing one-dimensional topological phases in waveguide lattices with broken chiral symmetry
• Virtual Topological Insulators with Real Quantized Physics
• The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps
• Topological edge states of quasiperiodic elastic metasurfaces
• Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices
• Constructing a Weyl semimetal by stacking one dimensional topological phases
• Simulating and exploring Weyl semimetal physics with cold atoms in a two-dimensional optical lattice
• Critical phase dualities in 1D exactly-solvable quasiperiodic models
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Topologically robust transport of entangled photons in a 2D photonic system
• Two-dimensional Thouless pumping of light in photonic moiré lattices
• Fractional quantization of the topological charge pumping in a one-dimensional superlattice
• Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices
• Observation of critical phase transition in a generalized Aubry-André-Harper model on a superconducting quantum processor with tunable couplers
• Landau-Zener topological quantum state transfer
• Non-abelian Thouless pumping in a photonic lattice
• Fibonacci optical lattices for tunable quantum quasicrystals
• Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions
• PT Symmetric Floquet Topological Phase
• Many-body localization in a quasiperiodic Fibonacci chain
• Fractional topological states of dipolar fermions in one-dimensional optical superlattices
• Topological states in quasicrystals
• Kibble-Zurek mechanism with a single particle: dynamics of the localization-delocalization transition in the Aubry-André model
• Topological Phase Transition Independent of System Non-Hermiticity
• Hofstadter butterfly of a quasicrystal
• Simulation and Detection of Photonic Chern Insulators in One-Dimensional Circuit Quantum Electrodynamics Lattice
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit
• Generalized Aubry-André-Harper model with p-wave superconducting pairing
• Anomalous transport through algebraically localized states in one-dimension
• Topological pumping in a Floquet-Bloch band
• Characterization of topological phase transitions via topological properties of transition points
• Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain
• Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice
• Topological edge states with ultracold atoms carrying orbital angular momentum in a diamond chain
• Plasmon-polaritonic quadrupole topological insulators
• Hidden dualities in 1D quasiperiodic lattice models
• Topological state transfer in Kresling origami
• Realization of quasicrystalline quadrupole topological insulators in electrical circuits
• Topological Edge Modes by Smart Patterning
• Non-Commutative Chern Numbers for Generic Aperiodic Discrete Systems
• Nonadiabatic Topological Energy Pumps with Quasiperiodic Driving
• Simulating Chern insulators on a superconducting quantum processor
• A comprehensive review on developments of synthetic dimensions
• Quenched dynamics and spin-charge separation in an interacting topological lattice
• Non-power-law universality in one-dimensional quasicrystals
• Critical properties of the many-particle (interacting) Aubry-André model ground-state localization-delocalization transition
• Direct prediction of corner state configurations from edge winding numbers in 2D and 3D chiral-symmetric lattice systems
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Kohn-Luttinger mechanism driven exotic topological superconductivity on the Penrose lattice
• Corner states and topological transitions in two-dimensional higher-order topological sonic crystals with inversion symmetry
• Phase spectroscopy of topological invariants in photonic crystals
• Topological Edge States with Zero Hall Conductivity in a Dimerized Hofstadter Model
• Laughlin's topological charge pump in an atomic Hall cylinder
• Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
• Chains with loops - synthetic magnetic fluxes and topological order in one-dimensional spin systems
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• High-order topological insulators from high-dimensional Chern insulators
• Adiabatic pumping via avoided crossings in stiffness modulated quasiperiodic beams
• Higher-order topological pumping and its observation in photonic lattices
• Topological growing of Laughlin states in synthetic gauge fields
• Stabilizing multiple topological fermions on a quantum computer
• Exploring Topology of 1D Quasiperiodic Metastructures through Modulated LEGO Resonators
• Generalized Aubry-André-Harper model with modulated hopping and $p$-wave pairing
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Topological transitions of interacting bosons in one-dimensional bi-chromatic optical lattices
• Two-dimensional nonlinear Thouless pumping of matter waves
• Localization and symmetry breaking in the quantum quasiperiodic Ising glass
• Topological superconductivity in quasicrystals
• Quantum simulation of topological zero modes on a 41-qubit superconducting processor
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Topological supermodes in photonic crystal fiber
• Quantum Charge Pumps with Topological Phases in Creutz Ladder
• Smart patterning for topological pumping of elastic surface waves
• Quantum Walks of Two Interacting Anyons in 1D Optical Lattices
• Topological Anderson insulators with different bulk states in quasiperiodic chains
• Quantum Hall phase emerging in an array of atoms interacting with photons
• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
• The non-commutative n-th Chern number
• Differential topology of semimetals
• Effect of disorder on topological charge pumping in the Rice-Mele model
• Topological charge pumping of bound bosonic pairs
• Topological edge states and Aharanov-Bohm caging with ultracold atoms carrying orbital angular momentum
• Witnessing topological Weyl semimetal phase in a minimal circuit-QED lattice
• Ring Structure in the Complex Plane: A Fingerprint of non-Hermitian Mobility Edge
• Topological quantum transport and spatial entanglement distribution via disordered bulk channel
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• Generating controllable type-II Weyl points via periodic driving
• Universal momentum-to-real-space mapping of topological singularities
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Interaction Induced Topological Charge Pump
• Boundary spin polarization as robust signature of topological phase transition in Majorana nanowires
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• Chern and Majorana Modes of Quasiperiodic Systems
• A Topology-Controlled Photonic Cavity Based on the Near-Conservation of the Valley Degree of Freedom
• A Natural Topological Insulator
• Topological Gaps by Twisting
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Fractional boundary charges in quantum dot arrays with density modulation
• Topological mechanics in quasicrystals
• Localization, $\mathcal{P}\mathcal{T}$-Symmetry Breaking and Topological Transitions in non-Hermitian Quasicrystals
• Topological photonic alloy
• Adiabatic currents for interacting electrons on a lattice
• Topological Anderson phase in quasi-periodic waveguide lattices
• Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
• Topological spin excitations in Harper-Heisenberg spin chains
• Interactions enable Thouless pumping in a nonsliding lattice
• Dephasing-induced mobility edges in quasicrystals
• Topological photonic orbital angular momentum switch
• Confining massless Dirac particles in two-dimensional curved space
• Local Topological Markers in Odd Dimensions
• Layer-Dependent Topological Phase in a Two-Dimensional Quasicrystal and Approximant
• Topological swing in Bloch oscillations
• Second Chern crystals in four-dimensional synthetic translation space with inherently nontrivial topology
• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• Quantum phases and topological properties of interacting fermions in one-dimensional superlattices
• Quantum many-body topology of quasicrystals
• Exciting Reflectionless Unidirectional Edge Modes in a Reciprocal Photonic Topological Insulator Medium
• Spontaneous topological pumping in non-Hermitian systems
• Topological Mott insulators of ultracold atomic mixtures induced by interactions in one-dimensional optical superlattices
• Gauge-induced Floquet topological states in photonic waveguides
• Topological properties of Floquet winding bands in a photonic lattice
• Many-body localization in the interpolating Aubry-André-Fibonacci model
• The fate of reentrant localization phenomenon in the one-dimensional dimerized quasiperiodic chain with long-range hopping
• Edge and bulk localization of Floquet topological superconductors
• Topologically quantized current in quasiperiodic Thouless pumps
• Non-Abelian Generalizations of the Hofstadter model: Spin-orbit-coupled Butterfly Pairs
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Liquid-crystal-based topological photonics
• Topological states and quantized current in helical molecules
• Non-diffracting states in one-dimensional Floquet photonic topological insulators
• Topological nature of magnetization plateaus in periodically modulated quantum spin chains
• Topological dynamics of gyroscopic and Floquet lattices from Newton's laws
• Biphoton entanglement of topologically-distinct modes
• Spin-selective transmission through a single-stranded magnetic helix
• Dynamically Emerging Topological Phase Transitions in Nonlinear Interacting Soliton Lattices
• Quantized Topological Anderson-Thouless Pump
• Multiple localization transitions and novel quantum phases induced by staggered on-site potential
• Exact edge, bulk and bound states of finite topological systems
• Efficient algorithm to compute the second Chern number in four dimensional systems
• Topological Random Fractals
• Creation and annihilation of mobile fractional solitons in atomic chains
• The New Phase due to Symmetry Protected Piecewise Berry Phases; Enhanced Pumping and Non-reciprocity in Trimer Lattices
• Fast, robust and amplified transfer of topological edge modes on time-varying mechanical chain
• Various Topological Mott insulators in strongly-interacting boson system in one-dimensional superlattice
• Localization Driven Quantum Sensing
• From fractional boundary charges to quantized Hall conductance
• Seeing bulk topological properties of band insulators in small photonic lattices
• Quantum phase transition between hyperuniform density distributions
• Hubbard Models for Quasicrystalline Potentials
• Topological Phase Transition and Charge Pumping in a One-Dimensional Periodically Driven Optical Lattice
• Topological Floquet edge states in periodically curved waveguides
• Nonadiabatic robust excitation transfer assisted by an imaginary gauge field
• Parity-Induced Thermalization Gap in Disordered Ring Lattices
• Nature of Protected Zero Energy States in Penrose Quasicrystals
• Fractal energy gaps and topological invariants in hBN/Graphene/hBN double moiré systems
• Fate of topological states in incommensurate generalized Aubry-André models
• Multi-particle quantum walks and Fisher information in one-dimensional lattices
• Quantum dynamics on a lossy non-Hermitian lattice
• Graded quasiperiodic metamaterials perform fractal rainbow trapping
• Rapid Exploration of Topological Band Structures using Deep Learning
• Reversal of quantised Hall drifts at non-interacting and interacting topological boundaries
• Engineering Dissipative Quasicrystals
• Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal
• Classifying transport behavior via current fluctuations in open quantum systems
• The K-Theoretic Bulk-Boundary Principle for Dynamically Patterned Resonators
• Four-dimensional topological lattices through connectivity
• Theory of quantum oscillations in quasicrystals: Quantizing spiral Fermi surfaces
• Engineering slow light and mode crossover in a fractal-kagome waveguide network
• Quantum Cluster Quasicrystals
• Phasonic Spectroscopy of a Quantum Gas in a Quasicrystalline Lattice
• Length scale formation in the Landau levels of quasicrystals
• Classical Dimers on Penrose Tilings
• Topological Properties of Ultracold Bosons in One-Dimensional Quasiperiodic Optical Lattice
• Simulation and measurement of the fractional particle number in one-dimensional optical lattices
• Topology of many-body edge and extended quantum states in an open spin chain: 1/3--plateau, Kosterlitz-Thouless transition, and Luttinger liquid
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Critical and Topological Phases of Dimerized Kitaev Chain in Presence of Quasiperiodic Potential
• Anomalous charge pumping in a one-dimensional optical superlattice
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Projected Topological Branes
• Hidden-symmetry-protected topological phases on a one-dimensional lattice
• Finite-temperature phases of trapped bosons in a two-dimensional quasiperiodic potential
• Time Quasilattices in Dissipative Dynamical Systems
• Two-dimensional optical quasicrystal potentials for ultracold atom experiments
• Quantum walks in commensurate off-diagonal Aubry-André-Harper model
• Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes
• Controlled charge and spin current rectifications in a spin polarized device
• Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis
• Rational Approximations of Quasi-Periodic Problems via Projected Green's Functions
• Damping transition in an open generalized Aubry-André-Harper model
• Particle current rectification in a quasi-periodic double-stranded ladder
• High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems
• Semiclassical Dynamics, Berry Curvature and Spiral Holonomy in Optical Quasicrystals
• Phase controlled metal-insulator transition in multi-leg quasiperiodic optical lattices
• Strongly interacting bosons in multi-chromatic potentials supporting mobility edges: localization, quasi-condensation and expansion dynamics
• Enhanced compressibility due to repulsive interaction in the Harper model
• Topologically Universal Spectral Hierarchies of Quasiperiodic Systems
• Topological phases and Anderson localization in off-diagonal mosaic lattices
• Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
• Constructing higher-order topological states in higher dimension
• Topological photonic Su-Schrieffer-Heeger-type coupler
• Observation of nonlinearity-controlled switching of topological edge states
• Quantum criticality in the disordered Aubry-André model
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Breakdown of quantization in nonlinear Thouless pumping
• Light-matter interactions near photonic Weyl points
• Mechanics and dynamics of two-dimensional quasiperiodic composites
• Topological pumping assisted by Bloch oscillations
• Tunable Topologically-protected Super- and Subradiant Boundary States in One-Dimensional Atomic Arrays
• Topological Insulator in an Atomic Liquid
• Effects of Dephasing on Quantum Adiabatic Pumping with Nonequilibrium Initial States
• Critical integer quantum Hall topology and the integrable Maryland model as a topological quantum critical point
• Quantum Emulation of Extreme Non-equilibrium Phenomena with Trapped Atoms
• Non-Hermitian topology and criticality in photonic arrays with engineered losses
• Josephson effect in a Fibonacci quasicrystal
• Thouless pumping in a driven-dissipative Kerr resonator array
• Dissipative nonequilibrium synchronization of topological edge states via self-oscillation
• Second-order topological modes in two-dimensional continuous media
• Quasiperiodicity and 2D Topology in 1D Charge Ordered Materials
• Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains
• Entangled multi-component 4D quantum Hall states from photonic crystal defects
• The Harper-Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling
• Equilibrium phases of two-dimensional bosons in quasi-periodic lattices
• Localization via Quasi-Periodic Bulk-Bulk Correspondence
• Topological Phases of Fermionic Ladders with Periodic Magnetic Fields
• Topological Transitions with an Imaginary Aubry-Andre-Harper Potential
• Thouless pumping and trapping of two-component gap solitons
• Phononic Topological States in 1D Quasicrystals
• Stabilization of Hubbard-Thouless pumps through nonlocal fermionic repulsion
• Quantum logical controlled-NOT gate in a lithium niobate-on-insulator photonic quantum walk
• Emergence of quasiperiodic Bloch wave functions in quasicrystals
• Engineering Interaction Dynamics in Active Resonant Photonic Structures
• Nematic Superconductivity and Its Critical Vestigial Phases in the Quasi-crystal
• Beyond the constant-mass Dirac physics: Solitons, charge fractionization, and the emergence of topological insulators in graphene rings
• Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
• Dimensional evolution between one- and two-dimensional topological phases
• Colloquium: Synthetic quantum matter in non-standard geometries
• Multi-frequency optical lattice for dynamic lattice-geometry control
• Topological charge pumping in quasiperiodic systems characterized by Bott index
• Nonlinear Thouless Pumping of Solitons Across an Impurity
• Bulk-boundary correspondance for Sturmian Kohmoto like models
• Topological superconductivity in Fibonacci quasicrystals
• Revealing the boundary Weyl physics of the four-dimensional Hall effect via phason engineering in metamaterials
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Majorana zero modes and their bosonization
• Reentrant topological transitions with Majorana end states in 1D superconductors by lattice modulation
• Topological pumping of quantum correlations
• Topological edge states at Floquet quantum criticality
• Floquet Engineering with Particle Swarm Optimization: Maximizing Topological Invariants
• Inducing a many-body topological state of matter through Coulomb-engineered local interactions
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Quantized Hall drift in a frequency-encoded photonic Chern insulator
• Quasidisorder Induced Topology
• Two-point spectroscopy of Fibonacci topoelectrical circuits
• Bulk soliton dynamics in bosonic topological insulators
• Haldane model on the Sierpiński gasket
• Bias induced circular spin current: Effects of environmental dephasing and disorder
• Electrical analogue of one-dimensional and quasi-one-dimensional Aubry-André-Harper lattices
• Persistent homology analysis of a generalized Aubry-André-Harper model
• Topology of rotating stratified fluids with and without background shear flow
• Time-dependent reflection at the localization transition
• Topological Floquet interface states in optical fibre loops
• Phonon-induced breakdown of Thouless pumping in the Rice-Mele-Holstein model
• Dynamical gauge fields with bosonic codes
• Quantum transport in a one-dimensional quasicrystal with mobility edges
• Quench dynamics in the Aubry-André-Harper model with \textit{p}-wave superconductivity
• Topological Mott Insulator with Bosonic Edge Modes in 1D Fermionic Superlattices
• Topological Phase Transitions from Harper to Fibonacci Crystals
• Versatile Braiding of Non-Hermitian Topological Edge States
• Hidden self-duality and exact mobility edges in quasiperiodic network models
• Quasiperiodic criticality and spin-triplet superconductivity in superconductor-antiferromagnet moire patterns
• Topological quantum optical states in quasiperiodic cold atomic chains
• Interacting Topological Insulators with Synthetic Dimensions
• Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
• Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation
• Linking topological features of the Hofstadter model to optical diffraction figures
• Nonlinearity-induced Fractional Thouless Pumping of Solitons
• Fractional Topological States in Quantum Spin Chains with Periodical Modulation
• Topological phonon polariton enhanced radiative heat transfer in bichromatic nanoparticle arrays mimicking Aubry-André-Harper model
• A higher-dimensional quasicrystalline approach to the Hofstadter and Fibonacci butterflies topological phase diagram and band conductance: symbolic sequences, Sturmian coding and self-similar rules at all magnetic fluxes
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
• Self-duality of One-dimensional Quasicrystals with Spin-Orbit Interaction
• Almost mobility edges and existence of critical regions in one-dimensional quasiperiodic lattices
• Effect of loss on the topological features of dimer chain described by the extended Aubry-André-Harper model
• Plateau transitions of spin pump and bulk-edge correspondence
• Cooper instability and superconductivity on the Penrose lattice
• Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
• Biorthogonal topological charge pumping in non-Hermitian systems
• Chiral and Non-Chiral Edge States in Quantum Hall Systems with Charge Density Modulation
• Three-body constrained bosons in double-well optical lattice
• Equivalence and superposition of real and imaginary quasiperiodicities
• Engineering magnetoresistance: A new perspective
• Topologically protected mid-gap states induced by impurity in one-dimensional superlattices
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• Helical transport in coupled resonator waveguides
• Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Interaction driven topological phase transitions of hardcore bosons on a two-leg ladder
• Maryland model in optical waveguide lattices
• Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays
• Optical Thouless pumping transport and nonlinear switching in a topological low-dimensional discrete nematic liquid crystal array
• Nonparaxiality-triggered Landau-Zener transition in topological photonic waveguides
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Probing the Topological Anderson Transition in Quasiperiodic Photonic Lattices via Chiral Displacement and Wavelength Tuning
• Topological bands in one-dimensional periodic potentials
• Disorder-Protected Quantum State Transmission through Helical Coupled-Resonator Waveguides
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Localization to delocalization transition in a double stranded helical geometry: Effects of conformation, transverse electric field and dynamics
• Closing of gaps and gap labeling and passage from molecular states to critical states in a 2D quasicrystal
• Topological Boundary States in 1D: An Effective Fabry-Perot Model
• Topological quantum interference in a pumped Su-Schrieffer-Heeger lattice
• Higher-dimensional Hofstadter butterfly on Penrose lattice
• Topological gap labeling with the third Chern numbers in three-dimensional quasicrystals
• Controlled probing of localization effects in the non-Hermitian Aubry-André model via topolectrical circuits
• Coexistence of 1D and 2D topology and genesis of Dirac cones in the chiral Aubry-André model
• Beating the aliasing limit with aperiodic monotile arrays
• Topological pumping induced by spatiotemporal modulation of interaction
• Topological crystalline protection in a photonic system
• Tutorial: From Topology to Hall Effects -- Implications of Berry Phase Physics
• Band alignment effect in the topological photonic alloy
• Quantum walks accompanied by spin flipping in one-dimensional optical lattices
• Topological edge states in a Rydberg composite
• Edge and corner superconductivity in a 2D topological model
• Relating Diffraction and Spectral Data of Aperiodic Tilings: Towards a Bloch theorem
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Fibonacci-Modulation-Induced Multiple Topological Anderson Insulators
• Effects of Disorder in the Fibonacci Quasicrystal
• Bulk-edge correspondence in topological transport and pumping
• Confined states and topological phases in two-dimensional quasicrystalline $\pi$-flux model
• Simulating and probing many-body quantum states in waveguide-QED systems with giant atoms
• Topological Domain Walls in Graphene Nanoribbons with Carrier Doping
• Macroscopic Zeno effect in Su-Schrieffer-Heeger photonic topological insulator
• Localization and topological transitions in generalized non-Hermitian SSH models
• Two-Dimensional Thouless Pumping of Ultracold Fermions in Obliquely Introduced Optical Superlattice
• Fractal Surface States in Three-Dimensional Topological Quasicrystals
• Dimerization, Trimerization and Quantum pumping
• Spinful Aubry-Andre model in a magnetic field: Delocalization facilitated by a weak spin-orbit coupling
• Nontrivial topology and localization in the double exchange model with possible applications to perovskite manganites
• Optimal design of fast topological pumping
• Topological Protection of Two-photon Quantum Correlation on a Photonic Chip
• Tunability of Spin-Dependent Secondary Topological Interface States Induced in an Optical Complex Superlattice
• Unconventional localization phenomena in a spatially non-uniform disordered material
• Topologically nontrivial states in one-dimensional nonlinear bichromatic superlattices
• Classical topological paramagnetism
• Edge state, bound state and anomalous dynamics in the Aubry-André-Haper system coupled to non-Markovian baths
• Robust unidirectional transport in a one-dimensional metacrystal with long-range hopping
• Topological gap solitons in a 1D non-Hermitian lattice
• Anderson Localization and Swing Mobility Edge in Curved Spacetime
• Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks
• The influence of localization transition on dynamical properties for an extended Aubry-André-Harper model
• Unconventional superfluidity of superconductivity on Penrose lattice
• Read-out of Quasi-periodic Systems using Qubits
• Critical analysis of multiple reentrant localization in an antiferromagnetic helix with transverse electric field: Hopping dimerization-free scenario
• The Fibonacci quasicrystal: case study of hidden dimensions and multifractality
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Spin filtering and switching action in a diamond network with magnetic-nonmagnetic atomic distribution
• Fractional transconductance via non-adiabatic topological Cooper pair pumping
• Topological photon pumping in quantum optical systems
• Edge state preparation in one dimensional lattice by quantum Lyapunov control
• Extended-localized transition in diffusive quasicrystals
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Controllable Floquet edge modes in a multi-frequency driving system
• Efficient algorithm to compute the Berry conductivity
• Imbalance for a family of one-dimensional incommensurate models with mobility edges
• Topology in quasicrystals
• Eigenmodal Analysis of Anderson Localization: Applications to Photonic Lattices and Bose-Einstein Condensates
• Artificial gauge fields in the t-z mapping for optical pulses: spatio-temporal wavepacket control and quantum Hall physics
• Loss-induced universal one-way transport in periodically driven systems
• Universal quantum noise in adiabatic pumping
• Equivalence classes of Fibonacci lattices and their similarity properties
• Nonadiabatic nonlinear non-Hermitian quantized pumping
• Topological origin of quantum mechanical vacuum transitions and tunneling
• Mode Delocalization in Disordered Photonic Chern Insulator
• Quasiperiodicity protects quantized transport in disordered systems without gaps
• Hong-Ou-Mandel Interference in a temporal-average-inversion-symmetric chain
• Topological phases of amorphous matter
• Analytical study of quasi-one dimensional flat band networks and slow light analogue
• Compressibility enhancement in an almost staggered interacting Harper model
• 4$\pi$ and 8$\pi$ dual Josephson effects induced by symmetry defects
• Visualising the connection between edge states and the mobility edge in adiabatic and non-adiabatic topological charge transport
• Sensing electrons during an adiabatic coherent transport passage
• Perturbative Analysis of Quasi-periodic Patterning of Transmon Quantum Computers: Enhancement of Many-Body Localization
• The odd-even effect of mosaic modulation period of quasi-periodic hopping on the Anderson localization in a one-dimensional lattice model
• Transition from nodal loop to nodal chain phase in a periodically modulated optical lattice
• Weyl superconductivity and quasiperiodic Majorana arcs in quasicrystals
• Differences between quantum and classical adiabatic evolution
• Symmetry induced selective excitation of topological states in SSH waveguide arrays
• Waves in almost-periodic particle chains
• Experimental Realization of Anti-Unitary Wave-Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics
• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• Topological Thouless pumping in arrays of coupled spin chains
• Hamiltonian Cycles on Ammann-Beenker Tilings
• Universality of Abelian and non-Abelian Wannier functions in one dimension
• Enhanced superconductivity and various edge modes in modulated $t$-$J$ chains
• Quantum Topological Boundary States in Quasi-crystal
• Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor
• Hofstadter-Toda spectral duality and quantum groups
• Exact mobility edges in quasiperiodic network models with slowly varying potentials
• Open dynamics in the Aubry-André-Harper model coupled to a finite bath: the influence of localization in the system and dimensionality of bath
• Photonic quadrupole topological phases in zero-dimensional cavity with synthetic dimensions
• Symmetry-protected Landau-Zener-Stückelberg-Majorana interference and non-adiabatic topological transport of edge states
• Synthesizing the Quantum Spin Hall Phase for Ultracold Atoms in Bichromatic Chiral Optical Ladders
• Quantum synchronization in one-dimensional topological systems
• Convection-modulated topological edge mode and extended-localized criticality in thermal metamaterials
• Quantitative analysis of interaction effects in generalized Aubry-Andŕe-Harper models
• The $\pi$ Berry Phase and Topological Excitation in Interacting Boson-Fermion Mixtures
• Generalized Aubry-Andre-Harper Models in Optical Superlattices
• Curved vortex surfaces in four-dimensional superfluids: II. Equal-frequency double rotations
• Asymmetric topological pumping in nonparaxial photonics
• Arboreal Obstructed Atomic Insulating and Metallic Phases of Fermions
• Absence of disordered Thouless pumps at finite frequency
• Quasiperiodic Quadrupole Insulators
• Visualizing topological transport
• Exploring Thouless Pumping in the Generalized Creutz Model: A Graphical Method and Modulation Schemes
• Topological charge and spin pumping in a semiconductor nanowire
• Topologically Protected Photonic Modes in Composite Quantum Hall/Quantum Spin Hall Waveguides
• Missing link between the 2D Quantum Hall problem and 1D quasicrystals
• Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
• Floquet-Anderson localization in the Thouless pump and how to avoid it
• Physical rendering of synthetic spaces for topological sound transport
• Topology and criticality in non-Hermitian multimodal optical resonators through engineered losses
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Nonlinear topological Toda quasicrystal
• Structural constraints on mobility edges in one-dimensional quasiperiodic systems
• Boosting Topological Zero Modes Using Elastomer Waveguide Arrays
• Sublattice signatures of transitions in a $\mathcal{P}\mathcal{T}$-symmetric dimer lattice
• Preparation of edge states by shaking boundaries
• Persistent current in an almost staggered Harper model
• Localization and Topology in Noncentrosymmetric Superconductors with Disorder
• Recent progress on disorder-induced topological phases
• Multiple reentrant topological windows induced by generalized Bernoulli disorder
• Quantum theory of fractional topological pumping of lattice solitons
• Non-Abelian interference of topological edge states
• Autoencoder-based analytic continuation method for strongly correlated quantum systems
• Reentrant localization in a quasiperiodic chain with correlated hopping sequences
• Family of self-dual quasicrystals with critical Phases
• Topological constraints on the electronic band structure of hexagonal lattice in a magnetic field
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping
• Gauge fields induced by curved spacetime
• Bias driven circular current in a ring nanojunction: Critical role of environmental interaction
• Reentrant topology and reverse pumping in a quasiperiodic flux ladder
• Mapping Chern numbers in quasi-periodic interacting spin chains
• The Josephson effect in Fibonacci superconductors
• Disorder driven topological phase transitions in 1D mechanical quasicrystals
• Anharmonic Effect of Adiabatic Quantum Pumping
• Topological adiabatic dynamics in classical mass-spring chains with clamps
• Bloch-Landau-Zener Oscillations in Moiré Lattices
• Density-wave tendency from a topological nodal-line perspective
• Tunneling-induced fractal transmission in Valley Hall waveguides
• Localization and topological signatures under periodic twisting
• Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation
• Realizing Topological Quantum Walks on NISQ Digital Quantum Computer
• Superconducting order parameter in aperiodic binary systems
• Quantum state transfer and maximal entanglement between distant qubits using a minimal quasicrystal pump
• Chiral Diffraction from Aperiodic Monotile Lattice
• Angular momentum-dependent topological transport and its experimental realization using a transmission line network
• A strong-driving toolkit for topological Floquet energy pumps with superconducting circuits
• Exploring Unconventional Features Of Light Dynamics In Aubrey-Andre-Harper Model Based Quasi-periodic Optical Lattices
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• One-dimensional topological quasiperiodic chain for directional wireless power transfer
• Floquet topological phases with high Chern numbers in a periodically driven extended Su-Schrieffer-Heeger model
• Simulating topological phases and topological phase transitions with classical strings
• Zak Phase Dislocations in Trimer Lattices
• Topological edge states and disorder robustness in one-dimensional off-diagonal mosaic lattices
• Ultralow radiative heat flux by Anderson localization in quasiperiodic plasmonic chains
• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions
• Metal-Insulator Coexistence and Gap-Crossing Domain-Wall Modes in an Aubry-André Model with Nonlocal Hopping
• Topological dynamics of adiabatic cat states
• Evolution of topological end states in the one-dimensional Kondo-Heisenberg model with site modulation
• Dephasing-enhanced performance in quasiperiodic thermal machines
• Mobility-edge-embedded Hofstadter butterfly from a tilt-induced quasiperiodic potential
• Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux
• Emergent aperiodicity in Bose-Bose mixtures induced by spin-dependent periodic potentials
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Quantum transport in quasi-periodic lattice systems in presence of Büttiker probes
• On the origin of energy gaps in quasicrystalline potentials
• Emergent topological properties in spatially modulated sub-wavelength barrier lattices