Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models

Abstract

The Aubry-André or Harper (AAH) model has been the subject of extensive theoretical research in the context of quantum localization. Recently, it was shown that one-dimensional quasicrystals described by the incommensurate AAH model has a nontrivial topology. In this Letter, we show that the commensurate off-diagonal AAH model is topologically nontrivial in the gapless regime and supports zero-energy edge modes. Unlike the incommensurate case, the nontrivial topology in the off-diagonal AAH model is attributed to the topological properties of the one-dimensional Majorana chain. We discuss the feasibility of experimental observability of our predicted topological phase in the commensurate AAH model.

5 pages + 1 page supplementary material

References in corpus (8)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• A lattice of double wells for manipulating pairs of cold atoms
• Orbital superfluidity in the $P$-band of a bipartite optical square lattice
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Sublattice addressing and spin-dependent motion of atoms in a double-well lattice
• A semi-Dirac point in the Hofstadter spectrum
• Majorana fermions in density modulated p-wave superconducting wires
• Zero modes, energy gap, and edge states of anisotropic honeycomb lattice in a magnetic field

Cited by in corpus (185)

• Non-Hermitian Physics
• Electronic and optical properties of strained graphene and other strained 2D materials: a review
• Synthetic Dimension in Photonics
• Topological phase transition in non-Hermitian quasicrystals
• Topological photonic crystals: physics, designs and applications
• Topological quantum matter with cold atoms
• Topological phases of generalized Su-Schrieffer-Heeger models
• Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Topological Phases in Non-Hermitian Aubry-André-Harper Models
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Topological phases and edge states in a non-Hermitian trimerized optical lattice
• Topological Phase Transitions and Thouless Pumping of Light in Photonic Waveguide Arrays
• 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
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Geometrical pumping with a Bose-Einstein condensate
• Anderson localization in the Non-Hermitian Aubry-André-Harper model with physical gain and loss
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Topological insulators and semimetals in classical magnetic systems
• Topological pumping of edge states via adiabatic passage
• Radiative topological states in resonant photonic crystals
• Measuring topological invariants from generalized edge states in polaritonic quasicrystals
• Topological Effects in Chiral Symmetric Driven Systems
• An atom optics approach to studying lattice transport phenomena
• Su-Schrieffer-Heeger chain with one pair of PT-symmetric defects
• Topological lasing and self-induced transparency in two level systems
• Topological equivalence of crystal and quasicrystal band structures
• Floquet topological semimetal phases of an extended kicked Harper model
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices
• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
• Edge-state instabilities of bosons in a topological band
• Observation of dynamical phase transitions in a topological nanomechanical system
• Constructing a Weyl semimetal by stacking one dimensional topological phases
• Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices
• Topological Mirror Insulators in One Dimension
• Edge states and topological insulating phases generated by curving a nanowire with Rashba spin-orbit coupling
• Engineering of topological state transfer and topological beam splitter in an even-size Su-Schrieffer-Heeger chain
• Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices
• Fibonacci optical lattices for tunable quantum quasicrystals
• Generalized Aubry-André-Harper model with p-wave superconducting pairing
• Spontaneous PT symmetry breaking in non-Hermitian coupled cavities array
• Anomalous transport through algebraically localized states in one-dimension
• Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain
• Externally controlled high degree of spin polarization and spin inversion in a conducting junction: Two new approaches
• Phase spectroscopy of topological invariants in photonic crystals
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Topological Edge States with Zero Hall Conductivity in a Dimerized Hofstadter Model
• Quantum simulation of topological zero modes on a 41-qubit superconducting processor
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Topological transitions of interacting bosons in one-dimensional bi-chromatic optical lattices
• Generalized Aubry-André-Harper model with modulated hopping and $p$-wave pairing
• Topological Anderson insulators with different bulk states in quasiperiodic chains
• PT Symmetric Floquet Topological Phase in SSH Model
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Topological photonic crystal fibers and ring resonators
• Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
• Novel mobility edges in the off-diagonal disordered tight-binding models
• System size dependent topological zero modes in coupled topolectrical chains
• Edge and bulk localization of Floquet topological superconductors
• Non-Hermitian quasicrystal in dimerized lattices
• Classification of crystalline insulators without symmetry indicators: atomic and fragile topological phases in twofold rotation symmetric systems
• Topological nature of magnetization plateaus in periodically modulated quantum spin chains
• Line nodes and surface Majorana flat bands in static and kicked p-wave superconducting Harper model
• Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice
• Spin-selective transmission through a single-stranded magnetic helix
• Various Topological Mott insulators in strongly-interacting boson system in one-dimensional superlattice
• Topological Floquet edge states in periodically curved waveguides
• Topological invariants to characterize universality of boundary charge in one-dimensionalinsulators beyond symmetry constraints
• Fate of topological states in incommensurate generalized Aubry-André models
• Observation of one-dimensional Dirac fermions in silicon nanoribbons
• Characterization of symmetry-protected topological phases in polymerized models by trajectories of Majorana stars
• Topological Microlaser with A non-Hermitian Topological Bulk
• Fast quantum transfer mediated by topological domain walls
• Topological cascade laser for frequency comb generation in $\mathcal{P}\mathcal{T}$-symmetric structures
• Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials
• Analytical solution of open crystalline linear 1D tight-binding models
• Surface charge theorem and topological constraints for edge states: An analytical study of one-dimensional nearest-neighbor tight-binding models
• Anomalous charge pumping in a one-dimensional optical superlattice
• Quantum walks in commensurate off-diagonal Aubry-André-Harper model
• Hidden-symmetry-protected topological phases on a one-dimensional lattice
• Spectral butterfly, mixed Dirac-Schrödinger fermion behavior and topological states in armchair uniaxial strained graphene
• Localization driven superradiant instability
• Projected Topological Branes
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Dynamical Scaling of Surface Roughness and Entanglement Entropy in Disordered Fermion Models
• Long-range entangled zero-mode state in a non-Hermitian lattice
• Generalized lattice Wilson-Dirac fermions in (1+1) dimensions for atomic quantum simulation and topological phases
• Particle current rectification in a quasi-periodic double-stranded ladder
• Damping transition in an open generalized Aubry-André-Harper model
• Many-body Aharonov-Bohm caging in a lattice of rings
• Topological phases and Anderson localization in off-diagonal mosaic lattices
• Controlled charge and spin current rectifications in a spin polarized device
• Phase controlled metal-insulator transition in multi-leg quasiperiodic optical lattices
• Quantum criticality in the disordered Aubry-André model
• Exact Mobility edges and topological Anderson insulating phase in a slowly varying quasiperiodic model
• Non-Hermitian topology and criticality in photonic arrays with engineered losses
• Simulating Z_2 topological insulators via a one-dimensional cavity optomechanical cells array
• A topological quantum pump in serpentine-shaped semiconducting narrow channels
• Topological Phases of Fermionic Ladders with Periodic Magnetic Fields
• Quasiperiodicity and 2D Topology in 1D Charge Ordered Materials
• Complete phase diagram and topological properties of interacting bosons in one-dimensional superlattices
• Novel topological insulators from crystalline symmetries
• Engineering topological phase transition and Aharonov-Bohm caging in a flux-staggered lattice
• Exact zero modes in a quantum compass chain under inhomogeneous transverse fields
• Topological Transitions with an Imaginary Aubry-Andre-Harper Potential
• Phononic Topological States in 1D Quasicrystals
• Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
• Reentrant topological transitions with Majorana end states in 1D superconductors by lattice modulation
• A numerical study of the localization transition of Aubry-André type models
• Floquet band engineering with Bloch oscillations
• Equivalence of Topological Insulators and Superconductors
• Electrical analogue of one-dimensional and quasi-one-dimensional Aubry-André-Harper lattices
• Quasidisorder Induced Topology
• Bias induced circular spin current: Effects of environmental dephasing and disorder
• Persistent homology analysis of a generalized Aubry-André-Harper model
• Antiferromagnetic helix as an efficient spin polarizer: Interplay between electric field and higher ordered hopping
• Topology of multiple cross-linked Su-Schrieffer-Heeger chains
• Topological phase detection through high-harmonic spectroscopy in extended Su-Schrieffer-Heeger chains
• Phase diagram of a generalized off-diagonal Aubry-André model with p-wave pairing
• Topological quantum optical states in quasiperiodic cold atomic chains
• Detecting topological phases via survival probabilities of edge Majorana fermions
• Hidden self-duality and exact mobility edges in quasiperiodic network models
• Topological Materials for Near-Field Radiative Heat Transfer
• Statistically induced topological phase transitions in a one-dimensional superlattice anyon-Hubbard model
• Topological phonon polariton enhanced radiative heat transfer in bichromatic nanoparticle arrays mimicking Aubry-André-Harper model
• Mobility Edges in one-dimensional Models with quasi-periodic disorder
• Scaling behavior in a multicritical one-dimensional topological insulator
• Engineering magnetoresistance: A new perspective
• Topological end states due to inhomogeneous strains in wrinkled semiconducting ribbons
• Topologically protected mid-gap states induced by impurity in one-dimensional superlattices
• Defects in Graphene : A Topological Description
• Floquet topological phase in a generalized PT-symmetric lattice
• Topological gap labeling with the third Chern numbers in three-dimensional quasicrystals
• Topological edge and corner states in coupled wave lattices in nonlinear polariton condensates
• Simulating and probing many-body quantum states in waveguide-QED systems with giant atoms
• Topological pumping induced by spatiotemporal modulation of interaction
• Controlled probing of localization effects in the non-Hermitian Aubry-André model via topolectrical circuits
• Topological crystalline protection in a photonic system
• Dimerization, Trimerization and Quantum pumping
• Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks
• Topological metals constructed by sliding quantum wire arrays
• Spinful Aubry-Andre model in a magnetic field: Delocalization facilitated by a weak spin-orbit coupling
• Read-out of Quasi-periodic Systems using Qubits
• Anderson Localization and Swing Mobility Edge in Curved Spacetime
• Thermoelectric phenomena in an antiferromagnetic helix: Role of electric field
• Unconventional localization phenomena in a spatially non-uniform disordered material
• Exotic odd-even parity effects in transmission phase, (Andreev) conductance, and shot noise of a dimer atomic chain by topology
• Barriers to Macroscopic Superfluidity and Insulation in a 2D Aubry-André Model
• Unveiling quantum criticality of disordered Aubry-André-Harper models via typical fidelity susceptibility
• Loss-induced universal one-way transport in periodically driven systems
• Topological end states in a one-dimensional spatially modulated interaction spinless fermion model
• Topological phase diagram of the disordered 2XY model in presence of generalized Dzyaloshinskii-Moriya Interaction
• Edge state preparation in one dimensional lattice by quantum Lyapunov control
• Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model
• A coupled Temperley-Lieb algebra for the superintegrable chiral Potts chain
• Topological states constructed by two different trivial quantum wires
• The odd-even effect of mosaic modulation period of quasi-periodic hopping on the Anderson localization in a one-dimensional lattice model
• Compressibility enhancement in an almost staggered interacting Harper model
• Topological Anderson insulator phases in one dimensional quasi-periodic mechanical SSH chains
• Exact mobility edges in quasiperiodic network models with slowly varying potentials
• Generalized Aubry-Andre-Harper Models in Optical Superlattices
• Universality of Abelian and non-Abelian Wannier functions in one dimension
• Quantum synchronization in one-dimensional topological systems
• Quantitative analysis of interaction effects in generalized Aubry-Andŕe-Harper models
• The $\pi$ Berry Phase and Topological Excitation in Interacting Boson-Fermion Mixtures
• Solitons induced by an in-plane magnetic field in rhombohedral multilayer graphene
• Preparation of edge states by shaking boundaries
• Nonlinear topological Toda quasicrystal
• Sublattice signatures of transitions in a $\mathcal{P}\mathcal{T}$-symmetric dimer lattice
• Missing link between the 2D Quantum Hall problem and 1D quasicrystals
• Topology and criticality in non-Hermitian multimodal optical resonators through engineered losses
• Engineering Topological Nodal Line Semimetals in Rashba Spin-Orbit Coupled Atomic Chains
• Dynamical signature of edge state in the 1D Aubry-André model
• Tunable zero modes and quantum interferences in flat-band topological insulators
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Quantum transport in quasi-periodic lattice systems in presence of Büttiker probes
• Realizing Topological Quantum Walks on NISQ Digital Quantum Computer