Quantized Electric Multipole Insulators

Abstract

In this article we extend the celebrated Berry-phase formulation of electric polarization in crystals to higher electric multipole moments. We determine the necessary conditions under which, and minimal models in which, the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they manifest topologically protected corner states carrying fractional charge, i.e., fractionalization at the boundary of the boundary. To characterize these new insulating phases of matter, we introduce a new paradigm whereby `nested' Wilson loops give rise to a large number of new topological invariants that have been previously overlooked. We propose three realistic experimental implementations of this new topological behavior that can be immediately tested.

arXiv commentMain text: 9 pages, 6 figures. Supplementary Material: 37 pages, 15 figures. Submitted on Jul 25, 2016

References in corpus (23)

• Maximally-localized generalized Wannier functions for composite energy bands
• Topological Field Theory of Time-Reversal Invariant Insulators
• Photonic Floquet Topological Insulators
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• Inversion Symmetric Topological Insulators
• Observation of the topological soliton state in the Su-Schrieffer-Heeger model
• Light propagation and localization in modulated photonic lattices and waveguides
• Hourglass Fermions
• Observation of novel edge states in photonic graphene
• Topological creation and destruction of edge states in photonic graphene
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
• Topological Insulators from Group Cohomology
• Edge modes in band topological insulators
• Atom-optics simulator of lattice transport phenomena
• Electric polarization in a Chern insulator
• An atom optics approach to studying lattice transport phenomena
• Berry-phase description of Topological Crystalline Insulators
• Universal sign-control of coupling in tight-binding lattices
• Surface polarization and edge charges

Cited by in corpus (1033)

• Non-Hermitian Physics
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• The (High Quality) Topological Materials In The World
• $(d-2)$-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
• Catalogue of Topological Electronic Materials
• 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
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Nonlinear topological photonics
• Direct observation of corner states in second-order topological photonic crystal slabs
• Topological protection of photonic mid-gap cavity modes
• Classical higher-order topological insulators
• Photonic quadrupole topological phases
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Second-order photonic topological insulator with corner states
• All "Magic Angles" Are "Stable" Topological
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Progress and prospects in magnetic topological materials
• Observation of second-order topological insulators in sonic crystals
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Topological acoustics
• Corner states of light in photonic waveguides
• High-throughput calculations of magnetic topological materials
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Non-Hermitian topological phenomena: A review
• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• Elastic higher-order topological insulator with topologically protected corner states
• Photonic crystal nanocavity based on a topological corner state
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Higher-order non-Hermitian skin effect
• New topological invariants in non-Hermitian systems
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Topological photonic crystals: physics, designs and applications
• Observation of higher-order non-Hermitian skin effect
• Two-dimensional second-order topological insulator in graphdiyne
• Topological Non-Hermitian skin effect
• Topological quantum matter with cold atoms
• Experimental discovery of bulk-disclination correspondence
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Majorana corner modes in a high-temperature platform
• Acoustic realization of quadrupole topological insulators
• Higher-order topological corner states induced by gain and loss
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Magnetic Topological Quantum Chemistry
• Active topological photonics
• Low-threshold topological nanolasers based on second-order corner state
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Higher-Order Topological Insulator in Twisted Bilayer Graphene
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• High-Temperature Majorana Corner States
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Non-Abelian band topology in noninteracting metals
• Classification of atomic-scale multipoles under crystallographic point groups and application to linear response tensors
• Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice
• Realization of an acoustic third-order topological insulator
• Higher-Order Topological Insulators in Quasicrystals
• Nonlinear second-order photonic topological insulators
• Lasing from multipole topological corner states
• A fractional corner anomaly reveals higher-order topology
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Higher Order Topological Phases: A General Principle of Construction
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Experimental Observation of Higher-Order Topological Anderson Insulators
• Observation of a higher-order topological bound state in the continuum
• Observation of Quadrupole Transitions and Edge Mode Topology in an LC network
• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Möbius Insulator and Higher-Order Topology in MnBi${}_{2n}$Te${}_{3n+1}$
• Weak-Pairing Higher Order Topological Superconductors
• Helical Topological Edge States in a Quadrupole Phase
• Topological Materials Discovery from Crystal Symmetry
• Majorana Kramers pairs in higher-order topological insulators
• Thouless pumping and topology
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Higher-Order Weyl Semimetals
• Non-linear second-order topological insulators
• Knots and Non-Hermitian Bloch Bands
• Second-order topological non-Hermitian skin effects
• Observation of an acoustic octupole topological insulator
• An anomalous higher-order topological insulator
• Topological Quadrupolar Semimetals
• Minimal model for higher-order topological insulators and phosphorene
• Engineering Corner States from Two-Dimensional Topological Insulators
• Demonstration of a 3rd order hierarchy of higher order topological states in a three-dimensional acoustic metamaterial
• Observation of a Majorana zero mode in a topologically protected edge channel
• Two-dimensional higher-order topology in monolayer graphdiyne
• Universal Approach to Magnetic Second-Order Topological Insulator
• Demonstration of a quantized acoustic octupole topological insulator
• Higher-order topological semimetal in acoustic crystals
• Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields
• Non-Hermitian route to higher-order topology in an acoustic crystal
• Higher-order Weyl Semimetals
• Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
• Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals
• Fractional disclination charge in two-dimensional $C_n-$symmetric topological crystalline insulators
• Bound states in the continuum of higher-order topological insulators
• Higher Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures
• Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices
• Dimensional Crossover of Topological Edge States in Su-Schrieffer-Heeger Model
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Observation of a phononic higher-order Weyl semimetal
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Rotation Anomaly and Topological Crystalline Insulators
• Liganded Xene as a Prototype of Two-Dimensional Stiefel-Whitney Insulators
• Helical Hinge Majoranas in Iron-Based Superconductors
• Symmetry Enforced Chiral Hinge States and Surface Quantum Anomalous Hall Effect in Magnetic Axion Insulator ${\text{Bi}}_{2-x}{\text{Sm}}_x{\text{Se}}_3$
• Topolectrical-circuit octupole insulator with topologically protected corner states
• Topological edge states of interacting photon pairs emulated in a topolectrical circuit
• Lattice models with exactly solvable topological hinge and corner states
• Topological phases without crystalline counterparts
• Floquet second-order topological insulators from nonsymmorphic space-time symmetries
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Many-Body Electric Multipole Operators in Extended Systems
• Higher-order topological insulators in amorphous solids
• Many-Body Order Parameters for Multipoles in Solids
• Quadrupole Topological Photonic Crystals
• Boundary-obstructed topological phases
• Topology of Disconnected Elementary Band Representations
• Higher-order topological odd-parity superconductors
• Controlling mass and energy diffusion with metamaterials
• A brief review of topological photonics in one, two, and three dimensions
• Dynamical Singularities of Floquet Higher-Order Topological Insulators
• Topological switch between second-order topological insulators and topological crystalline insulators
• Higher-order Floquet topological phases with corner and bulk bound states
• On the Remarkable Superconductivity of FeSe and its Close Cousins
• Coupled-wire construction of static and Floquet second-order topological insulators
• Higher-order topological insulators in synthetic dimensions
• First Principles Calculations for Topological Quantum Materials
• Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
• Band Representations and Topological Quantum Chemistry
• Topolectric circuits: Theory and construction
• Symmetry-protected hierarchy of anomalous multipole topological band gaps in nonsymmorphic metacrystals
• Mirror skin effect and its electric circuit simulation
• Superfluid weight bounds from symmetry and quantum geometry in flat bands
• Realization of the square-root higher-order topological insulator in electric circuits
• Hybrid-order topological insulators in a phononic crystal
• Second-order Topological Superconductors with Mixed Pairing
• Magnetic second-order topological insulators and semimetals
• Inversion-protected higher order topological superconductivity in monolayer WTe${}_2$
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Emergent Phases of Fractonic Matter
• Tutorial: Computing topological invariants in two-dimensional photonic crystals
• Fractional corner charges in spin-orbit coupled crystals
• Majorana corner modes and tunable patterns in an altermagnet heterostructure
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Realizing Su-Schrieffer-Heeger topological edge states in Rydberg-atom synthetic dimensions
• Higher-order photonic topological states in surface-wave photonic crystals
• Hybrid skin-topological modes without asymmetric couplings
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Higher-order Topological Anderson Insulators
• Lattice symmetry assisted second order topological superconductors and Majorana patterns
• Unsupervised Manifold Clustering of Topological Phononics
• Competition and interplay between topology and quasi-periodic disorder in Thouless pumping of ultracold atoms
• Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials
• Topological insulators and semimetals in classical magnetic systems
• Topological Semimetal Nanostructures: From Properties to Topotronics
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• Higher-order topological phases in tunable $C_3$-symmetric photonic crystals
• Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals
• Inner Skin Effects on Non-Hermitian Topological Fractals
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Hofstadter Topology: Non-crystalline Topological Materials at High Flux
• Geometric classification of non-Hermitian topological systems through the singularity ring
• Cavity Quantum Electrodynamics with Second-Order Topological Corner State
• Discovering new two-dimensional topological insulators from computational screening
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne
• Higher-order Topological Mott Insulators
• Engineering Fragile Topology in Photonic Crystals: Topological Quantum Chemistry of Light
• Generating a second-order topological insulator with multiple corner states by periodic driving
• Structural Disorder Induced Second-order Topological Insulators in Three Dimensions
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Acoustic Möbius insulators from projective symmetry
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Topological states in non-Hermitian two-dimensional Su-Schrieffer-Heeger model
• Semi-classical wave packet dynamics in non-uniform electric fields
• Proximity-induced Majorana hinge modes in antiferromagnetic topological insulators
• Square-root higher-order topological insulator on a decorated honeycomb lattice
• Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics
• Higher-order Dirac sonic crystals
• Topological states on fractal lattices
• Acoustic square-root topological insulators
• Lasing from complete set of topological states in two dimensional photonic crystal structure
• Creation and Manipulation of Higher-Order Topological States by Altermagnets
• Coupling between Exciton-Polariton Corner Modes through Edge States
• Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
• Gapped Topological Kink States and Topological Corner States in Graphene
• On-chip higher-order topological micromechanical metamaterials
• Higher-order topological superconductors in $\mathcal{P}$-, $\mathcal{T}$-odd quadrupolar Dirac materials
• Hyperbolic band topology with non-trivial second Chern numbers
• Braiding Majorana corner modes in a second-order topological superconductor
• Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons
• First- and Second-Order Topological Superconductivity and Temperature-Driven Topological Phase Transitions in the Extended Hubbard Model with Spin-Orbit Coupling
• Phase diagram of disordered higher-order topological insulator: A machine learning study
• Higher-order topological phases on fractal lattices
• Second-order topological phases protected by chiral symmetry
• Nonlinear imaging of nanoscale topological corner states
• On the robustness of topological corner modes in photonic crystals
• Four-Dimensional Higher-Order Chern Insulator and Its Acoustic Realization
• Nonlinearity induced topological physics in momentum space and real space
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Hierarchy of higher-order Floquet topological phases in three dimensions
• Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides
• Antiunitary symmetry protected higher order topological phases
• Topolectrical-circuit realization of 4D hexadecapole insulator
• Nonlinear imaging of nanoscale topological corner states
• $C_n$-symmetric higher-order topological crystalline insulators in atomically thin transition-metal dichalcogenides
• The existence of robust edge currents in Sierpinsky Fractals
• Sub-symmetry protected topological states
• Acoustic Higher-Order Weyl Semimetal with Bound Hinge States in the Continuum
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Boundary-obstructed topological high-T${}_c$ superconductivity in iron pnictides
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• General corner charge formula in two-dimensional C_n-symmetric higher-order topological insulators
• Quantum Metric and Correlated States in Two-dimensional Systems
• Vortex states in an acoustic Weyl crystal with a topological lattice defect
• Experimental identification of the second-order non-Hermitian skin effect with physics-graph-informed machine learning
• Higher-order topological phases in a spring-mass model on a breathing kagome lattice
• Measurement-only quantum computation with Majorana corner modes
• Anomalous topological edge states in non-Hermitian piezophononic media
• Phase tunable second-order topological superconductor
• Photonic quadrupole topological insulator using orbital-induced synthetic flux
• Floquet generation of Second Order Topological Superconductor
• Higher-Order Topological Dirac Superconductors
• 3D hinge transport in acoustic higher-order topological insulators
• Topological phases in ring resonators: recent progress and future prospects
• Topological Zak Phase in Strongly-Coupled LC Circuits
• Higher Order Topological Insulator via Periodic Driving
• Higher-Order Weyl-Exceptional-Ring Semimetals
• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• Fragile Phases As Affine Monoids: Classification and Material Examples
• Difficulties in operator-based formulation of the bulk quadrupole moment
• Twisted quadrupole topological photonic crystals
• Floquet higher order topological insulator in a periodically driven bipartite lattice
• All-electrically tunable networks of Majorana bound states
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Symmetry indicators of band topology
• Local invariants identify topology in metals and gapless systems
• A Universal Mirror-stacking Approach for Constructing Topological Bound States in the Continuum
• Stability of topological edge states under strong nonlinear effects
• Classification and construction of higher-order symmetry protected topological phases of interacting bosons
• Creating boundaries along a synthetic frequency dimension
• Second Order Topological Insulator State in Hexagonal Lattices and its Abundant Material Candidates
• Evidence for Helical Hinge Zero Modes in an Fe-Based Superconductor
• Partial lattice defects in higher order topological insulators
• Higher-order Dirac Semimetal in a Photonic Crystal
• Fractional Topological Superconductivity and Parafermion Corner States
• Room temperature electrically pumped topological insulator lasers
• Higher-order topological band structures
• Observation of symmetry protected zero modes in topolectrical circuits
• Floquet higher-order topological insulators and superconductors with space-time symmetries
• Inverse design of higher-order photonic topological insulators
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• Floquet Second-Order Topological Superconductor Driven via Ferromagnetic Resonance
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Non-Hermitian physics without gain or loss: the skin effect of reflected waves
• Higher-order topological superconductivity: possible realization in Fermi gases and Sr${}_2$RuO${}_4$
• Topological Materials Discovery By Large-order symmetry indicators
• Floquet second-order topological insulators in non-Hermitian systems
• Topological Phases of Photonic Crystals under Crystalline Symmetries
• First-principles theory of spatial dispersion: Dynamical quadrupoles and flexoelectricity
• Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators
• Detection of Topological Materials with Machine Learning
• Effective Model for Fractional Topological Corner Modes in Quasicrystals
• Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena
• Three-dimensional superconductors with hybrid higher order topology
• Nonlinear non-Hermitian higher-order topological laser
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• One-dimensional $2^n$-root topological insulators and superconductors
• Multi-orbital model reveals second-order topological insulator in 1H-transition metal dichalcogenide
• Kekule Lattice in Graphdiyne: Coexistence of Phononic and Electronic Higher-Order Band Topology
• Point-Defect-Localized Bound States in the Continuum in Photonic Crystals and Structured Fibers
• Quadrupole topological insulators in Ta2M3Te5 (M= Ni, Pd) monolayers
• Atomic limit and inversion-symmetry indicators for topological superconductors
• Proof of the bulk-edge correspondence through a link between topological photonics and fluctuation-electrodynamics
• Hierarchy of higher-order topological superconductors in three dimensions
• Theory of Topological Corner State Laser in Kagome Waveguide Arrays
• Temperature Dependent Electronic Structure in a Higher Order Topological Insulator Candidate EuIn${}_2$As${}_2$
• Majorana bound states in semiconducting nanostructures
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Quantization in chiral higher order topological insulators: circular dichroism and local Chern marker
• Two-dimensional Shiba lattices as possible platform for crystalline topological superconductivity
• Dislocation as a bulk probe of higher-order topological insulators
• Magnonic Quadrupole Topological Insulator in Antiskyrmion Crystals
• Splitting the hinge mode of higher-order topological insulators
• Engineering Non-Hermitian Skin Effect with Band Topology in Ultracold Gases
• Simple model for second-order topological insulators and loop-nodal semimetals in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Higher order topological superconductors as generators of quantum codes
• Bound states at partial dislocation defects in multipole higher-order topological insulators
• Wannier representation of Floquet topological states
• Strong and weak second-order topological insulators with hexagonal symmetry and ${\mathbb{Z}}_3$ index
• Topological Phases in Magnonics
• Plasmon-polaritonic quadrupole topological insulators
• Observation of supersymmetric pseudo-Landau levels in strained microwave graphene
• Systematic construction of square-root topological insulators and superconductors
• Realization of quasicrystalline quadrupole topological insulators in electrical circuits
• Reducing electronic transport dimension to topological hinge states by increasing geometry size of Dirac semimetal Josephson junctions
• Higher-order topological insulators in hyperbolic lattices
• Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
• Topological thermal transport
• Real space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems
• Higher-order topological solitonic insulators
• Topologically protected vortex transport via chiral-symmetric disclination
• Realization of a Z classified chiral-symmetric higher-order topological insulator in a coupling-inversion acoustic crystal
• Inversion-symmetry protected chiral hinge states in stacks of doped quantum Hall layers
• Majorana Corner Modes in a Second-Order Kitaev Spin Liquid
• Bulk-corner correspondence of time-reversal symmetric insulators: deduplicating real-space invariants
• Dislocation charges reveal two-dimensional topological crystalline invariants
• Majorana corner modes with solitons in an attractive Hubbard-Hofstadter model of cold atom optical lattices
• Theory of orbital magnetic quadrupole moment and magnetoelectric susceptibility
• Dual topology in Jacutingaite Pt${}_2$HgSe${}_3$
• Phonon-induced Floquet second-order topological phases protected by space-time symmetries
• Topological Invariant and Anomalous Edge Modes of Strongly Nonlinear Systems
• Computation of topological phase diagram of disordered Pb${}_{1-x}$Sn${}_x$Te using the kernel polynomial method
• Phononic real Chern insulator with protected corner modes in graphynes
• Direct prediction of corner state configurations from edge winding numbers in 2D and 3D chiral-symmetric lattice systems
• Zoology of non-Hermitian spectra and their graph topology
• Corner states and topological transitions in two-dimensional higher-order topological sonic crystals with inversion symmetry
• On the topological immunity of corner states in two-dimensional crystalline insulators
• Dual-Polarization Second-Order Photonic Topological Insulators
• Higher Order Bosonic Topological Phases in Spin Models
• Exact Higher-order Bulk-boundary Correspondence of Corner-localized States
• Higher-order topological states mediated by long-range coupling in $D_4$-symmetric lattices
• `Unhinging' the surfaces of higher-order topological insulators and superconductors
• High-order topological insulators from high-dimensional Chern insulators
• Experimental Detection of the Quantum Phases of a Three-Dimensional Topological Insulator on a Spin Quantum Simulator
• Observation of many-body Fock space dynamics in two dimensions
• Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
• Line nodes, Dirac points and Lifshitz transition in 2D nonsymmorphic photonic crystals
• Higher-order topological pumping and its observation in photonic lattices
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• Reentrant localization transition in the Su-Schrieffer-Heeger model with random-dimer disorder
• Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices
• Higher-order Topological Hyperbolic Lattices
• Higher-order topology in plasmonic kagome lattices
• Interaction-induced lattices for bound states: Designing flat bands, quantized pumps and higher-order topological insulators for doublons
• Detection of second-order topological superconductors by Josephson junctions
• Corner charge and bulk multipole moment in periodic systems
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Kramers Nodal Line Metals
• Simulation of Higher-Order Topological Phases and Related Topological Phase Transitions in a Superconducting Qubit
• Type-II quadrupole topological insulators
• First and Second Order Topological Phases on Ferromagnetic Breathing Kagome Lattice
• Three-dimensional higher-order topological acoustic system with multidimensional topological states
• Helical Liquids in Semiconductors
• Time-induced second-order topological superconductors
• Weyl nodes with higher-order topology in an optically driven nodal-line semimetal
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Non-Abelian braiding of Dirac fermionic modes using topological corner states in higher-order topological insulator
• Higher-order topology in monolayer graphene
• Entanglement polarization for the topological quadrupole phase
• Unconventional scaling at non-Hermitian critical points
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects
• Non-Abelian Bloch oscillations in higher-order topological insulators
• Chiral Hinge Magnons in Second-Order Topological Magnon Insulators
• Pfaffian formalism for higher-order topological insulators
• Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system
• Digital Simulation of Topological Matter on Programmable Quantum Processors
• Corner modes of the breathing kagome lattice: origin and robustness
• Cavity-mediated unconventional pairing in ultracold fermionic atoms
• Floquet Weyl semimetal phases in light-irradiated higher-order topological Dirac semimetals
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Non-Abelian hyperbolic band theory from supercells
• Majorana and parafermion corner states from two coupled sheets of bilayer graphene
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Edge-Corner Correspondence: Boundary-Obstructed Topological Phases with Chiral Symmetry
• Realization of Surface-Obstructed Topological Insulators
• Topological States in Generalized Electric Quadrupole Insulators
• Acoustic corner states in topological insulators with built-in Zeeman-like fields
• Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekulé Distortion
• Robustness of topological corner modes against disorder and application to acoustic networks
• Higher-Order Topological In-Bulk Corner State in Pure Diffusion Systems
• Ultra-sensitive integrated circuit sensors based on high-order nonHermitian topological physics
• Higher-order topological superconductors based on weak topological insulators
• Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal
• Valley-dependent Corner States in Honeycomb Photonic Crystal without Inversion Symmetry
• Vortex-line topology in iron-based superconductors with and without second-order topology
• Pairing Obstructions in Topological Superconductors
• Anomalous Quadrupole Topological Insulators in 2D Nonsymmorphic Sonic Crystals
• An operator-based approach to topological photonics
• Floquet Second Order Topological Superconductor based on Unconventional Pairing
• A Higher-Order Topological Insulator Phase in a Modulated Haldane Model
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Observation of Topological Corner State Arrays in Photonic Quasicrystals
• Magic-Angle Semimetals with Chiral Symmetry
• Fragile topologically flat band in the checkerboard antiferromagnetic monolayer FeSe
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• Axion coupling in the hybrid Wannier representation
• Localizing softness and stress along loops in three-dimensional topological metamaterials
• Systematic generation of the cascade of anomalous dynamical first and higher-order modes in Floquet topological insulators
• Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks
• High-throughput Investigations of Topological and Nodal Superconductors
• Higher-order topological Anderson insulators in quasicrystals
• Discovery of Higher-Order Topological Insulators using the Spin Hall Conductivity as a Topology Signature
• Topological edge and corner states in Bi fractals on InSb
• Local markers for crystalline topology
• Disorder-Induced Quantum Phase Transitions in Three-Dimensional Second-Order Topological Insulators
• Topological Superconductivity in an s-wave Superconductor and Its Implication to Iron-based Superconductors
• Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators
• Square-root topological phase with time-reversal and particle-hole symmetry
• Topology protects chiral edge currents in stochastic systems
• Majorana corner flat bands in two-dimensional second-order topological superconductors
• Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators
• Two-particle Berry phase mechanism for Dirac and Majorana Kramers pairs of corner modes
• Higher-order Fabry-Pérot Interferometer from Topological Hinge States
• Symmetry indicator in non-Hermitian systems
• Intrinsic first and higher-order topological superconductivity in a doped topological insulator
• Gauge Field Induced Chiral Zero Mode in Five-dimensional Yang Monopole Metamaterials
• Cornertronics in Two-Dimensional Second-Order Topological Insulators
• Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians
• Coulomb instabilities of 3D higher-order topological insulators
• Trapped state at a dislocation in a weak magnetomechanical topological insulator
• Dirac States in an Inclined Two-Dimensional Su-Schrieffer-Heeger Model
• Local Topological Markers in Odd Dimensions
• Delocalization Transition of Disordered Axion Insulator
• Buckled honeycomb group-$V$--$S_6$ symmetric $(d-2)$ higher order topological insulators
• General corner states in 2D SSH model with intracelluar next-nearest-neighbour hopping
• Non-Hermitian boundary spectral winding
• Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure
• The classification of surface states of topological insulators and superconductors with magnetic point group symmetry
• Gauge-induced Floquet topological states in photonic waveguides
• Higher-order topological insulators in antiperovskites
• The Global Phase Diagram of disordered Higher-order Weyl Semimetals
• Transition from metal to higher-order topological insulator driven by random flux
• Anti-chiral edge states and hinge states based on the Haldane model
• Piezoelectricity and Topological Quantum Phase Transitions in Two-Dimensional Spin-Orbit Coupled Crystals with Time-Reversal Symmetry
• Classification of crystalline insulators without symmetry indicators: atomic and fragile topological phases in twofold rotation symmetric systems
• Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
• Classification of Dirac points with higher-order Fermi arcs
• Matryoshka approach to Sine-Cosine topological models
• Second-order topological insulator in breathing square lattice of magnetic vortices
• Non-Abelian Generalizations of the Hofstadter model: Spin-orbit-coupled Butterfly Pairs
• Rotation Symmetry-Protected Topological Phases of Fermions
• Thouless Pumps and Bulk-Boundary Correspondence in Higher-Order Symmetry-Protected Topological Phases
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
• Observation of higher-order topological states on a quantum computer
• $N$-band Hopf insulator
• Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces
• Aspects of topological superconductivity in 2D systems: noncollinear magnetism, skyrmions, and higher-order topology
• Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Floquet higher-order Weyl and nexus semimetals
• Higher-order topological insulators in a magnetic field
• Quantum dynamical characterization and simulation of topological phases with high-order band inversion surfaces
• Higher-order valley vortices enabled by synchronized rotation in a photonic crystal
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Extended Bloch theorem for topological lattice models with open boundaries
• Microwave signature of robust topological Andreev-level crossings in superconducting proximitized crystalline Bi nanowires
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• Hinge solitons in three-dimensional second-order topological insulators
• Dynamical construction of Quadrupolar and Octupolar topological superconductors
• Euler Obstructed Cooper Pairing: Nodal Superconductivity and Hinge Majorana Zero Modes
• Comb tensor networks
• Quantized Topological Anderson-Thouless Pump
• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors
• Non-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals
• Higher-form Gauge Symmetries in Multipole Topological Phases
• Interaction driven surface Chern insulator in nodal line semimetals
• Edge states, corner states, and flat bands in a two-dimensional $\mathcal{P}\mathcal{T}$ symmetric system
• Flat bands and higher-order topology in polymerized triptycene: Tight-binding analysis on decorated star lattices
• Wannier-type photonic higher-order topological corner states induced solely by gain and loss
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Ferroelectric higher-order topological insulator in two dimensions
• Fractional Corner Charge of Sodium Chloride
• Boundaries of boundaries: a systematic approach to lattice models with solvable boundary states of arbitrary codimension
• Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence
• Engineering exotic second-order topological semimetals by periodic driving
• Theory of inversion-${\mathbb{Z}}_4$ protected topological chiral hinge states and its applications to layered antiferromagnets
• Topology invisible to eigenvalues in obstructed atomic insulators
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Topogivity: A Machine-Learned Chemical Rule for Discovering Topological Materials
• Hidden Breathing Kagome Topology in Hexagonal Transition Metal Dichalcogenides
• Topological excitonic corner states and nodal phase in bilayer quantum spin Hall insulators
• Topological Mechanics from Supersymmetry
• Hinged Quantum Spin-Hall Effect in Antiferromagnetic Topological Insulators
• Appearance of hinge states in second-order topological insulators via the cutting procedure
• Current-phase relation of a WTe2 Josephson junction
• Existence of Corner Modes in Elastic Twisted Kagome Lattices
• Higher-order topological spin Hall effect of sound
• Shift vector as the geometric origin of beam shifts
• The hybrid-order topology of weak topological insulators
• Quadrupole moments, edge polarizations, and corner charges in the Wannier representation
• Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
• Fractional Chiral Hinge Insulator
• Embedded Topological Insulators
• Second-order topological corner states in zigzag graphene nanoflake with different types of edge magnetic configurations
• Fragile phonon topology on the honeycomb lattice with time-reversal symmetry
• Edge states and corner modes in second-order topological phononic crystal plates
• Generation of higher-order topological insulators using periodic driving
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Higher-Order Topological Crystalline Insulating Phase and Quantized Hinge Charge in Topological Electride Apatite
• Simulation of higher-order topological phases in 2D spin-phononic crystal networks
• Time-reversal-invariant $C_2$-symmetric higher-order topological superconductors
• Magnon corner states in twisted bilayer honeycomb magnets
• Superconductors with anomalous Floquet higher-order topology
• Quadrupole spin polarization as signature of second-order topological superconductors
• Spin-Polarized Fractional Corner Charges and Their Photonic Realization
• Absence of topological protection of the interface states in ${\mathbb{Z}}_2$ photonic crystals
• Observation of backscattering induced by magnetism in a topological edge state
• Thermodynamic approach to electric quadrupole moments
• Second-order and real Chern topological insulator in twisted bilayer $\alpha$-graphyne
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Engineering second-order topological insulators via coupling two first-order topological insulators
• Many-Body Invariants for Chern and Chiral Hinge Insulators
• Klein-bottle quadrupole insulators and Dirac semimetals
• Optimization and robustness of topological corner state in second-order topological photonic crystal
• Breaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides
• Strain engineered higher order topological phases for spin-3/2 Luttinger fermions
• Floquet quadrupole photonic crystals protected by space-time symmetry
• Vortex solitons in topological disclination lattices
• Non-Compact Atomic Insulators
• Quasicrystalline second-order topological semimetals
• Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors
• Unified characterization for higher-order topological phase transitions
• Multidimensional sound propagation in 3D high-order topological sonic insulator
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
• $Z_4$ parafermion $\pm \pi /2$ modes in interacting periodically driven superconducting chain
• Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators
• Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
• Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries
• Topological edge and corner states and fractional corner charges in blue phosphorene
• Topological phases and Anderson localization in off-diagonal mosaic lattices
• Topological Superconductivity from Unconventional Band Degeneracy with Conventional Pairing
• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals
• Fractional corner charges in a 2D super-lattice Bose-Hubbard model
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Identifying Higher Order Topology and Fractional Corner Charge Using Entanglement Spectra
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Constructing higher-order topological states in higher dimension
• The Bulk-Hinge Correspondence and Three-Dimensional Quantum Anomalous Hall Effect in Second Order Topological Insulators
• Topological Crystalline Insulators with $C_2$ Rotation Anomaly
• Chiral Majorana Hinge Modes in Superconducting Dirac Materials
• Density-driven higher-order topological phase transitions in amorphous solids
• Universal signatures of Dirac fermions in entanglement and charge fluctuations
• Dual Topological Insulator Device with Disorder Robustness
• Weyl-like points from band inversions of spin-polarised surface states in NbGeSb
• Evidencing non-Bloch dynamics in temporal topolectrical circuits
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• Topological hinge modes in Dirac semimetals
• Robustness of Helical Hinge States of Weak Second-Order Topological Insulators
• Impurity bound states as detectors of topological band structures revisited
• Large shift current, $\pi$ Zak phase and unconventional nature in Se and Te
• ${\mathbb{Z}}_2$ Spin Hopf Insulator: Helical Hinge States and Returning Thouless Pump
• Measuring Zak phase in room-temperature atoms
• A Dirac fermion model associated with second order topological insulator
• Crystalline Responses for Rotation-Invariant Higher-Order Topological Insulators
• Engineering topological phases with a three-dimensional nodal-loop semimetal
• Discovering two-dimensional magnetic topological insulators by machine learning
• Higher-Order Topological Mott Insulator on the Pyrochlore Lattice
• Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant
• Robustness of chiral edge modes in fractal-like-lattices below two dimensions: A case study
• Higher-order topological superconductors from Weyl semimetals
• Topological properties of two-dimensional photonic square lattice without $C_4$ and $M_{x(y)}$ symmetries
• Lecture Notes on Topological Crystalline Insulators
• Boundary edge networks induced by bulk topology
• Higher-order Topological Phases of Magnons in van der Waals Honeycomb Ferromagnets
• Topological States in Two-Dimensional Su-Schrieffer-Heeger Models
• Multiplicative topological phases
• Phononic Stiefel-Whitney topology with corner vibrational modes in two-dimensional Xenes and ligand-functionalized derivatives
• Competition of non-Hermitian skin effect and topological localization of corner states observed in circuits
• Single-mode lasing based on PT-breaking of two-dimensional photonic higher-order topological insulator
• Escape from black holes in materials: Type II Weyl semimetals and generic edge states
• Topological states in a dimerized system with staggered magnetic fluxes
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics
• Second-order topological modes in two-dimensional continuous media
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Hinge states in a system of coupled Rashba layers
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• 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${}_2$
• Hybrid-order topological odd-parity superconductors via Floquet engineering
• Two-dimensional weak-type topological insulators in inversion symmetric crystals
• Topological transitions and Anderson localization of light in disordered atomic arrays
• Tunable two-dimensional laser arrays with zero-phase locking
• Symmetry-protected localized states at defects in non-Hermitian systems
• Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians
• Topological Edge and Interface states at Bulk disorder-to-order Quantum Critical Points
• Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
• Toeplitz operators on concave corners and topologically protected corner states
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Sublattice-sensitive Majorana Modes
• ${}^3$He Universe 2020
• Topological Transitions with an Imaginary Aubry-Andre-Harper Potential
• Majorana corner states on the dice lattice
• Role of the edges in a quasicrystalline Haldane model
• Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
• Theory of Dipole Insulators
• Topological corner modes in a brick lattice with nonsymmorphic symmetry
• Higher-order topological heat conduction on a lattice for detection of corner states
• Light bullets in Su-Schrieffer-Heeger photonic topological insulators
• Entanglement in a second order topological insulator on a square lattice
• Engineering topologically protected zero-dimensional interface end states in antiferromagnetic heterojunction graphene nanoflakes
• Engineering topological states and quantum-inspired information processing using classical circuits
• Robust zero modes in non-Hermitian systems without global symmetries
• High-Order Topological Phase Diagram Revealed by Anomalous Nernst Effect in Janus ScClI Monolayer
• Photonic nodal lines with quadrupole Berry curvature distribution
• Mirror real Chern insulator in two and three dimensions
• High-temperature Majorana corner modes in a $d+i{d}^{\prime }$ superconductor heterostructure: Application to twisted bilayer cuprate superconductors
• Topological phases of the dimerized Hofstadter butterfly
• Interaction-induced quantum spin Hall insulator in the organic Dirac electron system $\alpha$-(BEDT-TSeF)${}_2$I${}_3$
• Multi-frequency optical lattice for dynamic lattice-geometry control
• Hinge Magnons from Non-collinear Magnetic Order in Honeycomb Antiferromagnet
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• The General Principle behind Magnetization-induced Second-Order Topological Corner States in the Kane-Mele Model
• Dephasing enhanced strong Majorana zero modes in 2D and 3D higher-order topological superconductors
• Theory of edge states based on the hermiticity of tight-binding Hamiltonian operators
• Floquet second-order topological Anderson insulator hosting corner localized modes
• Dynamically characterizing topological phases by high-order topological charges
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Correlation Effects in Quadrupole Insulators: a Quantum Monte Carlo Study
• Lieb Schultz Mattis-Type Theorems and Other Non-perturbative Results for Strongly Correlated Systems with Conserved Dipole Moments
• Group theory study of the vibrational modes and magnetic order in the topological antiferromagnet MnBi${}_2$Te${}_4$
• Topological nature of higher-order hinge states revealed by spin transport
• Dirac cones and higher-order topology in quasi-continuous media
• Higher order topological matter and fractional chiral states
• Quantized charge-pumping in higher-order topological insulators
• Anomalous topological edge modes in a periodically-driven trimer lattice
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Effects of Disorder On Thouless Pumping In Higher-Order Topological Insulators
• Classification and construction of interacting fractonic higher-order topological phases
• Symmetry indicators in commensurate magnetic flux
• Transparent Josephson Junctions in Higher-Order Topological Insulator WTe2 via Pd Diffusion
• Effective field theories of topological crystalline insulators and topological crystals
• From magnetoelectric response to optical activity
• Magnetic Flux Periodicity in Second Order Topological Superconductors
• Chirality polarizations and spectral bulk-boundary correspondence
• Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
• Observation of emergent Dirac physics at the surfaces of acoustic higher-order topological insulators
• Topological Edge and Corner States in Biphenylene Network
• Persistence of Monoclinic Crystal Structure in Three-Dimensional Second-Order Topological Insulator Candidate 1T'-MoTe2 Thin Flake without Structural Phase transition
• Effective action approach to the filling anomaly in crystalline topological matter
• Tailoring Quadrupole Topological Insulators with Periodic Driving and Disorder
• Symmetric non-Hermitian skin effect with emergent nonlocal correspondence
• Observation of Dual-band Topological Corner Modes in Acoustic Kagome Lattice with Long-range Interactions
• Inducing a many-body topological state of matter through Coulomb-engineered local interactions
• Transport Induced Dimer State from Topological Corner States
• Observation of gapless corner modes in synthetic translation dimensions
• Interlayer Coupling Induced Topological Phase Transition to Higher Order
• Observation of topologically distinct corner states in "bearded" photonic Kagome lattices
• A General Method to Design Acoustic Higher-Order Topological Insulators
• High-order topological pumping on a superconducting quantum processor
• Topological d-wave superconductivity in two dimensions
• Third-order topological insulator induced by disorder
• Orbital shift-induced boundary obstructed topological materials with a large energy gap
• Dynamical Detection of Topological Spectral Density
• Topological Dipole Conserving Insulators and Multipolar Responses
• Towards a theory of surface orbital magnetization
• Multiple higher-order topological phases with even and odd pairs of zero-energy corner modes in a $C_3$ symmetry broken model
• Fully-Polarized Topological Isostatic Metamaterials in Three Dimensions
• Topological Corner States in Graphene by Bulk and Edge Engineering
• Controlling the Deformation of Metamaterials: Corner Modes via Topology
• Interacting topological mirror excitonic insulator in one dimension
• Aharonov-Bohm Effect in Three-dimensional Higher-order Topological Insulator
• Real-space Obstruction in Quantum Spin Hall Insulators
• Polarization-independent second-order photonic topological corner states
• Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
• Higher-order Skin Effect through a Hermitian-non-Hermitian Correspondence and Its Observation in an Acoustic Kagome Lattice
• Zeros of Green Functions in Topological Insulators
• Spin-polarized antichiral exciton-polariton edge states
• Topological and dynamical features of periodically driven spin ladders
• Topologically distinct atomic insulators
• Granular Graphene: direct observation of zigzag and armchair edge waves
• Single branch of chiral Majorana modes from doubly degenerate Fermi surfaces
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Topology with memory in nonlinear driven-dissipative photonic lattices
• Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
• Universal Higher-Order Topology from 5D Weyl semimetal: Edge topology, edge Hamiltonian and nested Wilson loop
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
• Analytical results for Green's functions of lattice fermions
• Generation of twisted magnons via spin-to-orbital angular momentum conversion
• Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines
• Topological phases of an interacting Majorana Benalcazar-Bernevig-Hughes model
• Two-Dimensional Higher-Order Topological Metals
• Qubit-photon corner states in all dimensions
• Network model for higher-order topological phases
• Zak Phase Induced Topological Nonreciprocity
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Rotational symmetry breaking and partial Majorana corner states in a high-Tc superconductor based heterostructure
• Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
• Thermodynamic electric quadrupole moments of nematic phases from first-principles calculation
• Abundance of second order topology in $C_3$ symmetric two-dimensional insulators
• Interlayer electric multipoles induced by in-plane field from quantum geometric origins
• Observation of nonlinear topological corner states originating from different spectral charges
• Spontaneous magnetization in unitary superconductors with time reversal symmetry breaking
• Hybrid-order topology in unconventional magnets of Eu-based Zintl compounds with surface-dependent quantum geometry
• Nonlinear Corner States in Topologically Nontrivial Kagome Lattice
• Connection topology of step edge state bands at the surface of a three dimensional topological insulator
• Hermitian chiral boundary states in non-Hermitian topological insulators
• Third-order topological insulator in three-dimensional lattice of magnetic vortices
• Revisiting (higher order and crystalline) topology in old models of lead telluride
• Mobile Kink Solitons in a Van der Waals Charge-Density-Wave Layer
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Out of equilibrium chiral higher order topological insulator on a $\pi$-flux square lattice
• Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation
• Simulating Floquet topological phases in static systems
• Magnetic field filtering of the hinge supercurrent in unconventional metal NiTe${}_2$-based Josephson junctions
• A Concise Review of Recently Synthesized 2D Carbon Allotropes: Amorphous Carbon, Graphynes, Biphenylene and Fullerene Networks
• On the relation of the entanglement spectrum to the bulk polarization
• Chiral orbital order of interacting bosons without higher bands
• Anomalous levitation and annihilation in Floquet topological insulators
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
• Entanglement Signature of Hinge Arcs, Fermi Arcs, and Crystalline Symmetry Protection in Higher-Order Weyl Semimetals
• Electric Polarization in Inhomogeneous Crystals
• Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model
• Topological obstructed atomic limit by annihilating Dirac fermions
• Protected Gapless Edge States In Trivial Topology
• Higher-order topological phase of interacting photon pairs
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Multi-Dimensional Quantum Walks: a Playground of Dirac and Schrödinger Particles
• Observation of Multiple Topological Corner States in Thermal Diffusion
• Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry
• Floquet higher-order topological phases in momentum space
• Wannier band transitions in disordered $\pi$-flux ladders
• Pseudo topological insulators
• Higher-order topological insulator in a modified Haldane-Hubbard model
• Green's Function Approach to Interacting Higher-order Topological Insulators
• Energy density as a probe of band representations in photonic crystals
• Versatile Control of Nonlinear Topological States in Non-Hermitian Systems
• Long-Time Magnetic Relaxation in Antiferromagnetic Topological Material EuCd${}_2$As${}_2$
• Robust Bulk States
• Higher-order topological superconductivity in monolayer WTe${}_2$ from repulsive interactions
• Holstein polaron in a pseudospin-$1$ quantum spin Hall system: first and second order topological phase transitions
• Gapless higher-order topology and corner states in Floquet systems
• Topological edge and corner states in coupled wave lattices in nonlinear polariton condensates
• Multi higher-order Dirac and nodal line semimetals
• Realizing Corner States in Artificial Crystals Based on Topological Spin Textures
• Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number
• AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
• Engineering Topological Models with a General-Purpose Symmetry-to-Hamiltonian Approach
• Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions
• Higher-order topological corner states induced solely by onsite potentials with mirror symmetry
• Controllable Weyl Nodes and Fermi Arcs from Floquet Engineering Triple Fermions
• Tunable boson-assisted finite-range interaction and engineering Majorana corner modes in optical lattices
• Transport features of topological corner states in honeycomb lattice with multihollow structure
• Multiorder topological superfluid phase transitions in a two-dimensional optical superlattice
• Crystalline-electromagnetic responses of higher order topological semimetals
• Higher-order topological insulators in a crisscross antiferromagnetic model
• Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems
• Effect of local Coulomb interaction on Majorana corner modes: weak and strong correlation limits
• Rotational Symmetry Protected Edge and Corner States in Abelian topological phases
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Second-order topological insulator under strong magnetic field: Landau levels, Zeeman effect, and magnetotransport
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Edge and corner superconductivity in a 2D topological model
• Spin-Dependent High-Order Topological Insulator and Two Types of Distinct Corner Modes in Monolayer FeSe/GdClO Heterostructure
• Dirac Solitons and Topological Edge States in the $\beta$-Fermi-Pasta-Ulam-Tsingou dimer lattice
• Controlling Majorana modes by $p$-wave pairing in two-dimensional $p+id$ topological superconductors
• Topological Classical Systems with Generalized Chiral Symmetry
• Bulk-boundary-transport correspondence of the second-order topological insulators
• Topological Corner Modes by Composite Wannier States in Glide-Symmetric Photonic Crystal
• Many-body multipole index and bulk-boundary correspondence
• A mono-atomic orbital-based 1D topological crystalline insulator
• Topological Insulators with Hybrid-order Boundary States
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Electric polarization and its quantization in one-dimensional non-Hermitian chains
• BerryEasy: A GPU enabled python package for diagnosis of nth-order and spin-resolved topology in the presence of fields and effects
• Competing topological phases in a non-Hermitian time-reversal symmetry-broken Bernevig-Hughes-Zhang model
• Corner and Edge States in Topological Sierpinski Carpet Systems
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Thermodynamics of a Higher-Order Topological Insulator
• Local and energy-resolved topological invariants for Floquet systems
• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
• Berezinskii-Kosterlitz-Thouless localization-localization transitions in disordered two-dimensional quantized quadrupole insulators
• Two-Dimensional Altermagnetic Iron Oxyhalides: Real Chern Topology and Valley-Spin-Lattice Coupling
• Extrinsic topology of Floquet anomalous boundary states in quantum walks
• Velocity Scanning Tomography for Room-Temperature Quantum Simulation
• Gapless Fermionic Systems as Phase-space Topological Insulators: Non-perturbative Results from Anomalies
• Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems
• Remote control of spin polarization of topological corner states
• Higher-order topology and corner triplon excitations in two-dimensional quantum spin-dimer models
• Hierarchical Topological States in Thermal Diffusive Networks
• Topological metals constructed by sliding quantum wire arrays
• Discovery of topological metamaterials by symmetry relaxation and smooth topological indicators
• Engineering rich two-dimensional higher-order topological phases by flux and periodic driving
• Takagi topological insulator with odd $\mathcal{P}\mathcal{T}$ pairs of corner states
• Higher-order topology in twisted multilayer systems: a review
• Fractional corner magnetization of collinear antiferromagnets
• Orbital Edelstein effect of electronic itinerant orbital motion at edges
• Emergent metallicity at the grain boundaries of higher-order topological insulators
• Structural, electronic and topological properties of 3D TmBi compound
• Generic Approach to Intrinsic Magnetic Second-order Topological Insulators via Inverted $p-d$ Orbitals
• Floquet chiral hinge modes and their interplay with Weyl physics in a three-dimensional lattice
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Chern dartboard insulator: sub-Brillouin zone topology and skyrmion multipoles
• Second-order topological insulator in a coinless discrete-time quantum walk
• Nontrivial gapless electronic states at the stacking faults of weak topological insulators
• Interaction-Driven Topological Switch in a $P$-Band Honeycomb Lattice
• Classification of topological invariants related to corner states
• Topological optical Raman superlattices
• Unconventional hybrid-order topological insulators
• Observation of nonlinear higher-order topological insulators with unconventional boundary truncations
• Zero-Energy State Localized near an Arbitrary Edge in Quadrupole Topological Insulators
• Topological reflection matrix
• Magnetic impurities along the edge of a quantum spin Hall insulator: Realizing a one-dimensional AIII insulator
• Tailoring higher-order topological phases via orbital hybridization
• Majorana corner pairs in a two-dimensional $s$-wave cold atomic superfluid
• Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence
• Additive rule of real and reciprocal space topologies at disclinations
• Chiral Hinge Transport in Disordered Non-Hermitian Second-Order Topological Insulators
• A compact and stable incidence-plane-rotating second harmonics detector
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• Second-order topology and supersymmetry in two-dimensional topological insulators
• Second Euler number in four dimensional synthetic matter
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Corner states of two-dimensional second-order topological insulators with a chiral symmetry and broken time reversal and charge conjugation
• Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect
• Higher-order topological superconductor phases in a multilayer system
• Topological electronic states in holey graphyne
• Topologically compatible non-Hermitian skin effect
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• On the role of geometric phase in the dynamics of elastic waveguides
• Topological Corner States in Bilayer and Trilayer Systems with Vertically Stacked Topological Heterostructures
• A topological current divider
• Characterization of higher-order topological superconductors using Bott indices
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• PHOENIX -- Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger equations with integrated extensions
• Two-dimensional orbital-obstructed insulators with higher-order band topology
• Distinguishing trivial and topological quadrupolar insulators by Wannier-Stark ladders
• Generalization of the Nested Wilson Loop Formalism in Topological Dirac Semimetals with Higher-order Fermi Arcs
• Second-order topological insulator in periodically driven lattice
• A new class of higher-order topological insulators that localize energy at arbitrary multiple sites
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Inexorable Edge Kondo Breakdown in Topological Kondo Insulators
• Exceptional second-order topological insulators
• Higher-order topology in honeycomb lattice with Y-Kekulé distortions
• Higher-order topological superconductors characterized by Fermi level crossings
• Scattering theory of higher order topological phases
• Second-order topological insulator in Bilayer borophene
• Anomalous in-gap edge states in two-dimensional pseudospin-1 Dirac insulators
• Boundary and defect criticality in topological insulators and superconductors
• Theoretical analysis of glide-Z_2 magnetic topological photonic crystals
• Pumping with Symmetry
• Optical Berry Curvature of Hinge State and Its Detection
• Spectral Form Factors of Topological Phases
• Theory of Josephson Current on a Magnetically Doped Topological Insulator
• Dimensional hierarchy of topological bound states in the continuum
• Hinge States of Second-Order Topological Insulators as a Mach-Zehnder Interferometer
• Corner Modes and Ground-State Degeneracy in Models with Gauge-Like Subsystem Symmetries
• Topological states constructed by two different trivial quantum wires
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Majorana corner states in square and Kagome quantum spin liquids
• Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
• Majorana modes in trapped-ion system and their Floquet engineering
• Recipe for higher-order topology on the triangular lattice
• Topological characteristics of gap closing points in nonlinear Weyl semimetals
• An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped Invariants related to corner states
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Engineering Hierarchical Symmetries
• Magnetic flux induced higher-order topological superconductivity
• Anisotropic Penetration Depths of Corner States in a Higher-Order Topological Insulator
• Topological phases in discrete stochastic systems
• Cavity-induced topological edge and corner states
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges
• Fragmented exceptional points and their bulk and edge realizations in lattice models
• Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides
• Quantized crystalline-electromagnetic responses in insulators
• Hermitian and non-Hermitian topology in active matter
• Higher order topological state induced by $d$-wave competing orders in high-T${}_c$ superconductor based heterostructure
• Finite-temperature topological invariant for higher-order topological insulators
• Hybrid symmetry class topological insulators
• Unconventional phonon spectra and obstructed edge phonon modes
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
• Mirror-symmetry protected higher-order topological zero-frequency boundary and corner modes in Maxwell lattices
• The destiny of obstructed atomic insulator under correlation
• Realization of a three-dimensional quantum Hall effect in a Zeeman-induced second order topological insulator on a torus
• Edge States with Hidden Topology in Spinner Lattices
• Topological parafermion corner states in clock-symmetric non-Hermitian second-order topological insulator
• Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices
• Unconventional Topological Insulators from Extended Topological Band Degeneracies
• Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model
• Selective branching, quenching, and converting of topological modes
• Topologically trivial gap-filling in superconducting Fe(Se,Te) by one dimensional defects
• Mixed-parity octupolar pairing and corner Majorana modes in three dimensions
• Higher-Order Topological Systems and Their Sub-Symmetry-Protected Topology
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants
• Topological semimetal with coexisting nodal points and nodal lines
• Revealing Higher-Order Topological Bulk-boundary Correspondence in Bismuth Crystal with Spin-helical Hinge State Loop and Proximity Superconductivity
• Altermagnetism and its induced higher-order topology on the Lieb lattice
• Dynamical characterization of topological phases beyond the minimal models
• Topological insulators and geometry of vector bundles
• Surface theory of a second-order topological insulator beyond the Dirac approximation
• Correlated second-order Dirac semimetals with Coulomb interactions
• Many-Body Quadrupolar Sum Rule for Higher-Order Topological Insulator
• Chiral Majorana Edge Modes and Vortex Majorana Zero Modes in Superconducting Antiferromagnetic Topological Insulator
• Floquet-Weyl semimetals generated by an optically resonant interband-transition
• Engineering Majorana corner modes from two-dimensional hexagonal crystals
• Perfectly localized Majorana corner modes in fermionic lattices
• Floquet-Anderson localization in the Thouless pump and how to avoid it
• Visualizing dissipative charge carrier dynamics at the nanoscale with superconducting charge qubit microscopy
• Inducing ${\mathbb{Z}}_2$ Topology in Twisted Nodal Superconductors
• Arboreal Obstructed Atomic Insulating and Metallic Phases of Fermions
• Topology reconstruction for asymmetric systems by isomorphic mapping or perturbation approximation
• Quasiperiodic Quadrupole Insulators
• C*-framework for higher-order bulk-boundary correspondences
• RKKY interaction in helical higher-order topological insulators
• Topological defect-mediated corner states and higher-order bulk topology in a two-dimensional crystalline insulator
• Dots and Boxes Algorithm for Peierls Substitution: Application to Multidomain Topological Insulators
• Breakdown of boundary criticality and exotic topological semimetals in $\mathcal{P}\mathcal{T}$-invariant systems
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Third-order Orbital Corner State and its Realization in Acoustic Crystals
• Cubic Dirac Semimetals: General Theory and Application to Rare-Earth Magnets
• Coexistence of gapless and gapped vortex modes with Majorana corner states in a 2D second-order topological superconductor
• Topological Aspects of Dirac Fermions in a Kagomé Lattice
• Multiple topological corner states in the continuum of extended kagome lattice
• Floquet Möbius topological insulators
• Exceptionally deficient topological square-root insulators
• Nonlinear quadrupole topological insulators
• Thresholdless corner vortex solitons in fractal Sierpiński topological insulators
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Spin separation and filtering assisted by topological corner states in the Kekulé lattice
• Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
• Topological Higgs Amplitude Modes in Strongly Interacting Superfluids
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Engineering Two-Dimensional Hybrid-Order Topological Insulators via Trilayer Coupling
• 3D Topologically Polarized Elastic Metamaterials Enable Asymmetric Energy Isolation at Low Frequencies
• Magnetic doping-induced second-order and first-order topological phase transition inthe photonic alloy
• Magnetic-flux tunable electronic transport through domain walls in a three-dimensional second-order topological insulator
• Non-Hermitian topological filters
• Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders
• The Quadrupole Moment of Higher-Order Topological Insulator at Finite temperature
• Nonlinearity-induced corner states in a kagome lattice
• Fractional chiral second-order topological insulator from a three-dimensional array of coupled wires
• Intrinsic higher-order topological states in 2D honeycomb Z_2 quantum spin Hall insulators
• Extended Haldane model -- a modern gateway to topological insulators
• Topological edge states of continuous Hamiltonians
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Fate of chiral order and impurity self-pinning in flat bands with local symmetry
• Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Network model for magnetic higher-order topological phases
• Quantum-vacuum-protected topological edge polaritons
• Crystalline finite-size topology
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Obstructed Atomic Insulators and Superfluids of Fermions Coupled to ${\mathbb{Z}}_2$ Gauge Fields
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Current switching behavior mediated via hinge modes in higher-order topological phases using altermagnets
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Recent progress on disorder-induced topological phases
• Single $\pi$-flux hosting topological defect modes in bilayer acoustic metamaterials
• Hofstadter Butterflies in Topological Insulators
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Code CFTs and Topological Matter
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Higher-order topological phases protected by noninvertible and subsystem symmetries
• Graphyne as a second-order and real Chern topological insulator in two dimensions
• Topological phases of monolayer and bilayer depleted Lieb lattices
• Symmetry-protected topological wire in a topological vacuum
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn
• Altermagnetism-induced higher-order topological Dirac semimetals in two-dimensional nonsymmorphic systems
• Non-Hermitian physics and topological phenomena in convective thermal metamaterials
• Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems
• Topological Photonics on a Small Scale
• Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups
• Three-dimensional higher-order topological insulator protected by cubic symmetry
• Theoretical description of interface states in a tetragonal lattice of bianisotropic resonators
• Magnetically tuned topological phase in graphene nanoribbon heterojunctions
• Layer-number parity induced topological phase transition
• Corner Flat Bands Induced by $d$-Density Wave and Partial Corner State Modification Due to Competition with $d$-Wave Superconductivity
• Vortex bound states in dimerized $\pi$-flux optical lattices: characterization, state preparation and current measurement
• Higher-order topological insulator in cubic semiconductor quantum wells
• Floquet first- and higher-order topological superconductors: A review
• Emergent One-Dimensional Helical Channel in Higher-Order Topological Insulators with Step Edges
• Boundary Condition Analysis of First and Second Order Topological Insulators
• Weak ${\mathbb{Z}}_2$ Supertopology
• Application of Jordan Decomposition to Non-Hermitian Lattice Models with Spectrally-Isolated Lower Dimensional States
• Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values
• Hinge modes of three-dimensional Euler insulators
• Floquet second-order topological insulator in strained graphene
• Second-order topological insulator induced by compensated altermagnetism without bulk spin splitting
• Topological defects in a double-mirror quadrupole insulator displace diverging charge
• Dynamics of 2D topological quadrupole insulator and Chern insulator induced by real-space topological changes
• Proposal for realizing and probing topological crystalline insulators in optical lattices
• Valley- and Orbital-Controlled 2D Chern Insulators Without Spin-orbit Interaction
• Anti-higher-order Weyl semimetal
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
• Supermetal-insulator transition in a non-Hermitian network model
• Coupled-wire construction of non-Abelian higher-order topological phases
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries
• Topologically nontrivial flat bands and quantum Hall crossovers in square-octagon lattice materials
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
• Higher-order topological quantum paramagnets
• Non-Hermitian second-order topological insulator with point gap
• Orbital Frontiers: Harnessing Higher Modes in Photonic Simulators
• When Wannier centers jump: Critical points between atomic insulating phases
• Nanoimprinted topological laser in the visible
• Topological energy pumping in a quasi-periodically driven four-level system
• Classification of topological insulators and superconductors with multiple order-two point group symmetries
• Non-Hermitian Higher-Order Dirac Semimetals
• Semimetals without correspondence between the topological charge of nodal line/surface and Fermi arc
• Synchronized in-gap edge states and robust copropagation in topological insulators without magnetic flux
• Non-Hermitian Higher-Order Weyl Semimetals
• Dynamical Symmetry Indicators for Floquet Crystals