Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models

Abstract

Higher-order topological phases of matter have been extensively studied in various areas of physics. While the Aubry-André-Harper model provides a paradigmatic example to study topological phases, it has not been explored whether a generalized Aubry-André-Harper model can exhibit a higher-order topological phenomenon. Here, we construct a two-dimensional higher-order topological insulator with chiral symmetry based on the Aubry-André-Harper model. We find the coexistence of zero-energy and nonzero energy corner-localized modes. The former is protected by the quantized quadrupole moment, while the latter by the first Chern number of the Wannier band. The nonzero-energy mode can also be viewed as the consequence of a Chern insulator localized on a surface. More interestingly, the non-zero energy corner mode can lie in the continuum of extended bulk states and form a bound state in the continuum of higher-order topological systems. We finally propose an experimental scheme to realize our model in electric circuits. Our study opens a door to further study higher-order topological phases based on the Aubry-André-Harper model.

arXiv comment10 pages, including supplemental material

References in corpus (70)

• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological nature of bound states in the radiation continuum
• Topological States and Adiabatic Pumping in Quasicrystals
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Acoustic higher-order topological insulator on a Kagome lattice
• Higher-Order Topology in Bismuth
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Topolectrical circuits
• Photonic quadrupole topological phases
• Observation of second-order topological insulators in sonic crystals
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Edge states and topological phases in one-dimensional optical superlattices
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Majorana corner modes in a high-temperature platform
• Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Higher-Order Topological Insulator in Twisted Bilayer Graphene
• High-Temperature Majorana Corner States
• Realization of an acoustic third-order topological insulator
• Higher-Order Topological Insulators in Quasicrystals
• Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology
• Higher Order Topological Phases: A General Principle of Construction
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Weak-Pairing Higher Order Topological Superconductors
• Coexistence of quantized and non-quantized geometric phases in quasi-one-dimensional systems without inversion symmetry
• Helical Topological Edge States in a Quadrupole Phase
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Topological Phases in Non-Hermitian Aubry-André-Harper Models
• An anomalous higher-order topological insulator
• Topological Quadrupolar Semimetals
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Electronic transport through a parallel--coupled triple quantum dot molecule: Fano resonances and bound states in the continuum
• Demonstration of a quantized acoustic octupole topological insulator
• Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
• Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
• Bound states in the continuum of higher-order topological insulators
• Higher Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures
• Rotation Anomaly and Topological Crystalline Insulators
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Topolectrical-circuit octupole insulator with topologically protected corner states
• Probing the Berry Curvature and Fermi Arcs of a Weyl Circuit
• Boundary Green functions of topological insulators and superconductors
• Many-Body Electric Multipole Operators in Extended Systems
• Many-Body Order Parameters for Multipoles in Solids
• Higher-order topological odd-parity superconductors
• Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Lattice symmetry assisted second order topological superconductors and Majorana patterns
• Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• Controlling Fano and Dicke effects via a magnetic flux in a double quantum-dot molecule
• Topological Amorphous Metals
• Second-order topological phases protected by chiral symmetry
• Topological protection of bound states against the hybridization
• Generalized Aubry-André-Harper model with p-wave superconducting pairing
• Higher Order Bosonic Topological Phases in Spin Models
• Optical analogue of population trapping in the continuum: classical and quantum interference effects
• Localized states in the continuum in low-dimensional systems
• Topological Corner States on Kagome Lattice Based Chiral Higher-Order Topological Insulator

Cited by in corpus (43)

• Experimental Observation of Higher-Order Topological Anderson Insulators
• Higher-Order Weyl Semimetals
• Higher-order Weyl Semimetals
• Topolectric circuits: Theory and construction
• Higher-order Topological Anderson Insulators
• Higher-order topological phases in tunable $C_3$-symmetric photonic crystals
• Structural Disorder Induced Second-order Topological Insulators in Three Dimensions
• Higher-order Dirac sonic crystals
• On-chip higher-order topological micromechanical metamaterials
• Hierarchy of higher-order Floquet topological phases in three dimensions
• Higher-Order Weyl-Exceptional-Ring Semimetals
• Floquet second-order topological insulators in non-Hermitian systems
• Higher-order Topological Hyperbolic Lattices
• Higher-order topology in monolayer graphene
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• A Higher-Order Topological Insulator Phase in a Modulated Haldane Model
• General corner states in 2D SSH model with intracelluar next-nearest-neighbour hopping
• Hinge solitons in three-dimensional second-order topological insulators
• Engineering exotic second-order topological semimetals by periodic driving
• Many-Body Invariants for Chern and Chiral Hinge Insulators
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Constructing higher-order topological states in higher dimension
• Higher-order topological superconductors from Weyl semimetals
• Second-Order Topological Insulator in Two-Dimensional C2N and Its Derivatives
• Second-Order Topological Insulator in van der Waals Heterostructures of CoBr${}_2$/Pt${}_2$HgSe${}_3$/CoBr${}_2$
• Topolectrical-circuit realization of quadrupolar surface semimetals
• Dephasing enhanced strong Majorana zero modes in 2D and 3D higher-order topological superconductors
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Effects of Disorder On Thouless Pumping In Higher-Order Topological Insulators
• Transport Induced Dimer State from Topological Corner States
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Higher-order topological insulator in a modified Haldane-Hubbard model
• Crystalline-electromagnetic responses of higher order topological semimetals
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Higher-order topology in twisted multilayer systems: a review
• Localization, transport and edge states in a two-strand ladder network in an aperiodically staggered magnetic field
• Generalized Aubry-Andre-Harper Models in Optical Superlattices
• Finite-temperature topological invariant for higher-order topological insulators
• Intermediate super-exponential localization with Aubry-André chains
• Topological defect-mediated corner states and higher-order bulk topology in a two-dimensional crystalline insulator
• The Quadrupole Moment of Higher-Order Topological Insulator at Finite temperature
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering