Higher-Order Topological Insulators

Abstract

Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of three-dimensional topological insulators to systems that host no gapless surface states, but exhibit topologically protected gapless hinge states. Their topological character is protected by spatio-temporal symmetries, of which we present two cases: (1) Chiral higher-order topological insulators protected by the combination of time-reversal and a four-fold rotation symmetry. Their hinge states are chiral modes and the bulk topology is ${\mathbb{Z}}_2$-classified. (2) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs and the bulk topology is $\mathbb{Z}$-classified. We provide the topological invariants for both cases. Furthermore we show that SnTe as well as surface-modified Bi${}_2$TeI, BiSe, and BiTe are helical higher-order topological insulators and propose a realistic experimental setup to detect the hinge states.

8 pages (4 figures) and 16 pages supplemental material (7 figures)

References in corpus (13)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Crystalline Insulators
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Robust spin-polarized midgap states at step edges of topological crystalline insulators
• Prototypical topological orbital ferromagnet $\gamma$-FeMn

Cited by in corpus (923)

• Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• The (High Quality) Topological Materials In The World
• Catalogue of Topological Electronic Materials
• Acoustic higher-order topological insulator on a Kagome lattice
• Higher-Order Topology in Bismuth
• 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
• Direct observation of corner states in second-order topological photonic crystal slabs
• Classical higher-order topological insulators
• Photonic quadrupole topological phases
• Second-order photonic topological insulator with corner states
• 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
• Corner states of light in photonic waveguides
• High-throughput calculations of magnetic topological materials
• Irvsp: to obtain irreducible representations of electronic states in the VASP
• Higher-order non-Hermitian skin effect
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• 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
• Two-dimensional second-order topological insulator in graphdiyne
• Topological quantum matter with cold atoms
• Experimental discovery of bulk-disclination correspondence
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Majorana corner modes in a high-temperature platform
• Higher-order topological corner states induced by gain and loss
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Magnetic Topological Quantum Chemistry
• Higher-Order Topological Insulator in Twisted Bilayer Graphene
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• High-Temperature Majorana Corner States
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Realization of an acoustic third-order topological insulator
• Higher-Order Topological Insulators in Quasicrystals
• Nonlinear second-order photonic topological insulators
• A fractional corner anomaly reveals higher-order topology
• Higher Order Topological Phases: A General Principle of Construction
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• 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
• 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
• Efficient Topological Materials Discovery Using Symmetry Indicators
• Topological Materials Discovery from Crystal Symmetry
• Majorana Kramers pairs in higher-order topological insulators
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Topological Superconductivity in Two-Dimensional Altermagnetic Metals
• Higher-Order Weyl Semimetals
• 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
• Two-dimensional higher-order topology in monolayer graphdiyne
• Universal Approach to Magnetic Second-Order Topological Insulator
• Higher-order topological semimetal in acoustic crystals
• 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
• 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
• 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
• Altermagnetic Routes to Majorana Modes in Zero Net Magnetization
• Topolectrical-circuit octupole insulator with topologically protected corner states
• Symmetry Enforced Chiral Hinge States and Surface Quantum Anomalous Hall Effect in Magnetic Axion Insulator ${\text{Bi}}_{2-x}{\text{Sm}}_x{\text{Se}}_3$
• Helical Hinge Majoranas in Iron-Based Superconductors
• Topological edge states of interacting photon pairs emulated in a topolectrical circuit
• Topological phases without crystalline counterparts
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Floquet second-order topological insulators from nonsymmorphic space-time symmetries
• 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
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
• Controlling mass and energy diffusion with metamaterials
• Higher-order topological odd-parity superconductors
• 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
• 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
• Non-Hermitian second-order skin and topological modes
• Room-temperature quantum spin Hall edge state in a higher-order topological insulator Bi${}_4$Br${}_4$
• Mirror skin effect and its electric circuit simulation
• Topological and geometrical aspects of band theory
• Second-order Topological Superconductors with Mixed Pairing
• Hybrid-order topological insulators in a phononic crystal
• Inversion-protected higher order topological superconductivity in monolayer WTe${}_2$
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Tutorial: Computing topological invariants in two-dimensional photonic crystals
• Fractional corner charges in spin-orbit coupled crystals
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Majorana corner modes and tunable patterns in an altermagnet heterostructure
• Higher-order photonic topological states in surface-wave photonic crystals
• Parity-Time Symmetry in Non-Hermitian Complex Optical Media
• 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
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• Topological insulators and semimetals in classical magnetic systems
• Topological Semimetal Nanostructures: From Properties to Topotronics
• Topological quantum phase transitions retrieved through unsupervised machine learning
• Higher-order topological phases in tunable $C_3$-symmetric photonic crystals
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Hofstadter Topology: Non-crystalline Topological Materials at High Flux
• Discovering new two-dimensional topological insulators from computational screening
• Symmetry-Enforced Weyl Phonons
• Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• 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
• Stiefel-Whitney classes and topological phases in band theory
• Structural Disorder Induced Second-order Topological Insulators in Three Dimensions
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Square-root higher-order topological insulator on a decorated honeycomb lattice
• Proximity-induced Majorana hinge modes in antiferromagnetic topological insulators
• Unified understanding of symmetry indicators for all internal symmetry classes
• Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics
• Topological states on fractal lattices
• Acoustic square-root topological insulators
• Higher-order Dirac sonic crystals
• Creation and Manipulation of Higher-Order Topological States by Altermagnets
• Topological Anderson Insulator in electric circuits
• Coupling between Exciton-Polariton Corner Modes through Edge States
• Evidence for Higher order topology in Bi and Bi${}_{0.92}$Sb${}_{0.08}$
• On-chip higher-order topological micromechanical metamaterials
• Braiding Majorana corner modes in a second-order topological superconductor
• Higher-order topological superconductors in $\mathcal{P}$-, $\mathcal{T}$-odd quadrupolar Dirac materials
• First- and Second-Order Topological Superconductivity and Temperature-Driven Topological Phase Transitions in the Extended Hubbard Model with Spin-Orbit Coupling
• Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons
• Second-order topological phases protected by chiral symmetry
• Phase diagram of disordered higher-order topological insulator: A machine learning study
• 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
• Nonlinear imaging of nanoscale topological corner states
• Hierarchy of higher-order Floquet topological phases in three dimensions
• Antiunitary symmetry protected higher order topological phases
• 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
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Acoustic Higher-Order Weyl Semimetal with Bound Hinge States in the Continuum
• 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
• 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
• Phase tunable second-order topological superconductor
• Measurement-only quantum computation with Majorana corner modes
• Higher-Order Topological Dirac Superconductors
• Floquet generation of Second Order Topological Superconductor
• 3D hinge transport in acoustic higher-order topological insulators
• Bulk and surface electronic structure of the dual-topology semimetal Pt2HgSe3
• Higher-Order Weyl-Exceptional-Ring Semimetals
• Higher Order Topological Insulator via Periodic Driving
• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• Fragile Phases As Affine Monoids: Classification and Material Examples
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Difficulties in operator-based formulation of the bulk quadrupole moment
• Twisted quadrupole topological photonic crystals
• All-electrically tunable networks of Majorana bound states
• Floquet higher order topological insulator in a periodically driven bipartite lattice
• Machine learning for materials discovery: two-dimensional topological insulators
• Symmetry indicators of band topology
• Classification and construction of higher-order symmetry protected topological phases of interacting bosons
• Second Order Topological Insulator State in Hexagonal Lattices and its Abundant Material Candidates
• Higher-order Dirac Semimetal in a Photonic Crystal
• Partial lattice defects in higher order topological insulators
• Higher-order topological band structures
• Fractional Topological Superconductivity and Parafermion Corner States
• Floquet Second-Order Topological Superconductor Driven via Ferromagnetic Resonance
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Observation of symmetry protected zero modes in topolectrical circuits
• Floquet higher-order topological insulators and superconductors with space-time symmetries
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• 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
• Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators
• Floquet second-order topological insulators in non-Hermitian systems
• Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena
• Effective Model for Fractional Topological Corner Modes in Quasicrystals
• Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• Topological states in quasicrystals
• Multi-orbital model reveals second-order topological insulator in 1H-transition metal dichalcogenide
• Nonlinear non-Hermitian higher-order topological laser
• Three-dimensional superconductors with hybrid higher order topology
• Dimensional transmutation from non-Hermiticity
• Hierarchy of higher-order topological superconductors in three dimensions
• Quadrupole topological insulators in Ta2M3Te5 (M= Ni, Pd) monolayers
• Theory of Topological Corner State Laser in Kagome Waveguide Arrays
• Atomic limit and inversion-symmetry indicators for topological superconductors
• Kekule Lattice in Graphdiyne: Coexistence of Phononic and Electronic Higher-Order Band Topology
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Temperature Dependent Electronic Structure in a Higher Order Topological Insulator Candidate EuIn${}_2$As${}_2$
• Majorana bound states in semiconducting nanostructures
• Topological classification and diagnosis in magnetically ordered electronic materials
• Purely rotational symmetry-protected topological crystalline insulator $\alpha$-Bi4Br4
• 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
• Quantization in chiral higher order topological insulators: circular dichroism and local Chern marker
• Splitting the hinge mode of higher-order topological insulators
• Higher order topological superconductors as generators of quantum codes
• Bound states at partial dislocation defects in multipole higher-order topological insulators
• Simple model for second-order topological insulators and loop-nodal semimetals in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
• Topological Phases in Magnonics
• Plasmon-polaritonic quadrupole topological insulators
• Realization of quasicrystalline quadrupole topological insulators in electrical circuits
• Symmetry indicators for topological superconductors
• Reducing electronic transport dimension to topological hinge states by increasing geometry size of Dirac semimetal Josephson junctions
• Higher-order topological insulators in hyperbolic lattices
• Systematic construction of square-root topological insulators and superconductors
• Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
• Higher-order topological solitonic insulators
• Observation of dynamical degeneracy splitting for the non-Hermitian skin effect
• Realization of a Z classified chiral-symmetric higher-order topological insulator in a coupling-inversion acoustic crystal
• Topological thermal transport
• Real space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems
• Majorana Corner Modes in a Second-Order Kitaev Spin Liquid
• Inversion-symmetry protected chiral hinge states in stacks of doped quantum Hall layers
• Bulk-corner correspondence of time-reversal symmetric insulators: deduplicating real-space invariants
• Phonon-induced Floquet second-order topological phases protected by space-time symmetries
• Dual topology in Jacutingaite Pt${}_2$HgSe${}_3$
• Computation of topological phase diagram of disordered Pb${}_{1-x}$Sn${}_x$Te using the kernel polynomial method
• Majorana corner modes with solitons in an attractive Hubbard-Hofstadter model of cold atom optical lattices
• Zoology of non-Hermitian spectra and their graph topology
• Direct prediction of corner state configurations from edge winding numbers in 2D and 3D chiral-symmetric lattice systems
• On the topological immunity of corner states in two-dimensional crystalline insulators
• Phononic real Chern insulator with protected corner modes in graphynes
• Dual-Polarization Second-Order Photonic Topological Insulators
• Corner states and topological transitions in two-dimensional higher-order topological sonic crystals with inversion symmetry
• Exact Higher-order Bulk-boundary Correspondence of Corner-localized States
• From atomic layer to the bulk: low-temperature atomistic structure, ferroelectric and electronic properties of SnTe films
• Higher Order Bosonic Topological Phases in Spin Models
• Higher-order topological states mediated by long-range coupling in $D_4$-symmetric lattices
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Higher-order topological pumping and its observation in photonic lattices
• `Unhinging' the surfaces of higher-order topological insulators and superconductors
• Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices
• Higher-order Topological Hyperbolic Lattices
• Reentrant localization transition in the Su-Schrieffer-Heeger model with random-dimer disorder
• Kramers Nodal Line Metals
• Interaction-induced lattices for bound states: Designing flat bands, quantized pumps and higher-order topological insulators for doublons
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Subdimensional topologies, indicators and higher order phases
• First and Second Order Topological Phases on Ferromagnetic Breathing Kagome Lattice
• High-throughput search for magnetic topological materials using spin-orbit spillage, machine-learning and experiments
• Helical Liquids in Semiconductors
• Weyl nodes with higher-order topology in an optically driven nodal-line semimetal
• Simulation of Higher-Order Topological Phases and Related Topological Phase Transitions in a Superconducting Qubit
• Type-II quadrupole topological insulators
• Time-induced second-order topological superconductors
• Non-Abelian Bloch oscillations in higher-order topological insulators
• Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system
• Non-Abelian braiding of Dirac fermionic modes using topological corner states in higher-order topological insulator
• Demonstration of acoustic high-order Stiefel-Whitney semimetal in bilayer graphene sonic crystals
• Experimental observation of non-Hermitian higher-order skin interface states in topological electric circuits
• Entanglement polarization for the topological quadrupole phase
• Chiral Hinge Magnons in Second-Order Topological Magnon Insulators
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Pfaffian formalism for higher-order topological insulators
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Cavity-mediated unconventional pairing in ultracold fermionic atoms
• Edge-Corner Correspondence: Boundary-Obstructed Topological Phases with Chiral Symmetry
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Topological synchronization of quantum van der Pol oscillators
• Floquet Weyl semimetal phases in light-irradiated higher-order topological Dirac semimetals
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Dropping an impurity into a Chern insulator: a polaron view on topological matter
• Comprehensive scan for nonmagnetic Weyl semimetals with nonlinear optical response
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Majorana and parafermion corner states from two coupled sheets of bilayer graphene
• Fractional charge bound to a vortex in two dimensional topological crystalline insulators
• Realization of Surface-Obstructed Topological Insulators
• Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekulé Distortion
• Acoustic corner states in topological insulators with built-in Zeeman-like fields
• Topological States in Generalized Electric Quadrupole Insulators
• Robustness of topological corner modes against disorder and application to acoustic networks
• Higher-Order Topological In-Bulk Corner State in Pure Diffusion Systems
• Vortex-line topology in iron-based superconductors with and without second-order topology
• Higher-order topological superconductors based on weak topological insulators
• Pairing Obstructions in Topological Superconductors
• Floquet Second Order Topological Superconductor based on Unconventional Pairing
• Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal
• Fully relativistic $GW$/Bethe-Salpeter calculations in BerkeleyGW: implementation, symmetries, benchmarking, and performance
• Teleportation of Berry curvature on the surface of a Hopf insulator
• Anomalous Quadrupole Topological Insulators in 2D Nonsymmorphic Sonic Crystals
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Fragile topologically flat band in the checkerboard antiferromagnetic monolayer FeSe
• Axion coupling in the hybrid Wannier representation
• Topological electronic structure and spin texture of quasi-one-dimensional higher-order topological insulator Bi4Br4
• Topological photonic crystal fibers based on second-order corner modes
• Realizing Hopf Insulators in Dipolar Spin Systems
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• Systematic generation of the cascade of anomalous dynamical first and higher-order modes in Floquet topological insulators
• High-throughput Investigations of Topological and Nodal Superconductors
• Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks
• Higher-order topological Anderson insulators in quasicrystals
• Discovery of Higher-Order Topological Insulators using the Spin Hall Conductivity as a Topology Signature
• Majorana corner flat bands in two-dimensional second-order topological superconductors
• 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
• Topological crystalline insulator states in the Ca${}_2$As family
• Transport response of topological hinge modes in $\alpha$-Bi${}_4$Br${}_4$
• Delocalization Transition of Disordered Axion Insulator
• Higher-order Fabry-Pérot Interferometer from Topological Hinge States
• Coulomb instabilities of 3D higher-order topological insulators
• Room-Temperature Topological Phase Transition in Quasi-One-Dimensional Material Bi${}_4$I${}_4$
• Symmetry indicator in non-Hermitian systems
• Two-particle Berry phase mechanism for Dirac and Majorana Kramers pairs of corner modes
• Cornertronics in Two-Dimensional Second-Order Topological Insulators
• Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians
• Dirac States in an Inclined Two-Dimensional Su-Schrieffer-Heeger Model
• Geometric orbital magnetization in adiabatic processes
• The Global Phase Diagram of disordered Higher-order Weyl Semimetals
• General corner states in 2D SSH model with intracelluar next-nearest-neighbour hopping
• Higher-order topological insulators in antiperovskites
• Gauge-induced Floquet topological states in photonic waveguides
• Buckled honeycomb group-$V$--$S_6$ symmetric $(d-2)$ higher order topological insulators
• The classification of surface states of topological insulators and superconductors with magnetic point group symmetry
• Geometric and nongeometric contributions to the surface anomalous Hall conductivity
• Classification of Dirac points with higher-order Fermi arcs
• Transition from metal to higher-order topological insulator driven by random flux
• Anti-chiral edge states and hinge states based on the Haldane model
• Rotation Symmetry-Protected Topological Phases of Fermions
• 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
• Light-induced half-quantized Hall effect and axion insulator
• Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
• Second-order topological insulator in breathing square lattice of magnetic vortices
• Discovery of a hybrid topological quantum state in an elemental solid
• $N$-band Hopf insulator
• Doubled Quantum Spin Hall Effect with High-Spin Chern Number in $\alpha$-Antimonene and $\alpha$-Bismuthene
• Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
• Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery
• Long-range hopping and indexing assumption in one-dimensional topological insulators
• Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
• Higher-order valley vortices enabled by synchronized rotation in a photonic crystal
• Intrinsic Magnetic Topological Materials
• Floquet higher-order Weyl and nexus semimetals
• Extended Bloch theorem for topological lattice models with open boundaries
• Symmetry Analysis of Anomalous Floquet Topological Phases
• Quantum dynamical characterization and simulation of topological phases with high-order band inversion surfaces
• Microwave signature of robust topological Andreev-level crossings in superconducting proximitized crystalline Bi nanowires
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Higher-order topological insulators in a magnetic field
• Topologically nontrivial Andreev bound states
• Higher-form Gauge Symmetries in Multipole Topological Phases
• Dynamical construction of Quadrupolar and Octupolar topological superconductors
• Sliding Ferroelectrics Induced Hybrid-Order Topological Phase Transitions
• Euler Obstructed Cooper Pairing: Nodal Superconductivity and Hinge Majorana Zero Modes
• Hinge solitons in three-dimensional second-order topological insulators
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Edge states, corner states, and flat bands in a two-dimensional $\mathcal{P}\mathcal{T}$ symmetric system
• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors
• Interaction driven surface Chern insulator in nodal line semimetals
• Flat bands and higher-order topology in polymerized triptycene: Tight-binding analysis on decorated star lattices
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Ferroelectric higher-order topological insulator in two dimensions
• Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence
• Engineering exotic second-order topological semimetals by periodic driving
• Boundaries of boundaries: a systematic approach to lattice models with solvable boundary states of arbitrary codimension
• Fractional Corner Charge of Sodium Chloride
• Symmetry-enforced Band Nodes in 230 Space Groups
• Hinged Quantum Spin-Hall Effect in Antiferromagnetic Topological Insulators
• Topological Mechanics from Supersymmetry
• Current-phase relation of a WTe2 Josephson junction
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Appearance of hinge states in second-order topological insulators via the cutting procedure
• Existence of Corner Modes in Elastic Twisted Kagome Lattices
• Topology invisible to eigenvalues in obstructed atomic insulators
• Theory of inversion-${\mathbb{Z}}_4$ protected topological chiral hinge states and its applications to layered antiferromagnets
• Topological excitonic corner states and nodal phase in bilayer quantum spin Hall insulators
• Higher-order topological spin Hall effect of sound
• The hybrid-order topology of weak topological insulators
• Embedded Topological Insulators
• Edge states and corner modes in second-order topological phononic crystal plates
• Generation of higher-order topological insulators using periodic driving
• Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
• Controlling a quantum point junction on the surface of an antiferromagnetic topological insulator
• Fractional Chiral Hinge Insulator
• Floquet Engineering Ultracold Polar Molecules to Simulate Topological Insulators
• Second-order topological corner states in zigzag graphene nanoflake with different types of edge magnetic configurations
• Quadrupole spin polarization as signature of second-order topological superconductors
• Superconductors with anomalous Floquet higher-order topology
• Magnon corner states in twisted bilayer honeycomb magnets
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• Fast quantum transfer mediated by topological domain walls
• 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
• Spin-Polarized Fractional Corner Charges and Their Photonic Realization
• Many-Body Invariants for Chern and Chiral Hinge Insulators
• Klein-bottle quadrupole insulators and Dirac semimetals
• Breaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Engineering second-order topological insulators via coupling two first-order topological insulators
• Absence of topological protection of the interface states in ${\mathbb{Z}}_2$ photonic crystals
• Magnetoconductance, Quantum Hall Effect, and Coulomb Blockade in Topological Insulator Nanocones
• Optimization and robustness of topological corner state in second-order topological photonic crystal
• Second-order and real Chern topological insulator in twisted bilayer $\alpha$-graphyne
• Unified characterization for higher-order topological phase transitions
• Axion Insulator State in Hundred-Nanometer-Thick Magnetic Topological Insulator Sandwich Heterostructures
• Rules for dissipationless topotronics
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Multidimensional sound propagation in 3D high-order topological sonic insulator
• Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors
• Strain engineered higher order topological phases for spin-3/2 Luttinger fermions
• Quasicrystalline second-order topological semimetals
• Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
• Quench dynamics and scaling laws in topological nodal loop semimetals
• Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Topological Crystalline Insulators with $C_2$ Rotation Anomaly
• Fractional corner charges in a 2D super-lattice Bose-Hubbard model
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals
• Topological Superconductivity from Unconventional Band Degeneracy with Conventional Pairing
• The Bulk-Hinge Correspondence and Three-Dimensional Quantum Anomalous Hall Effect in Second Order Topological Insulators
• Identifying Higher Order Topology and Fractional Corner Charge Using Entanglement Spectra
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Universal signatures of Dirac fermions in entanglement and charge fluctuations
• Corner states, hinge states and Majorana modes in SnTe nanowires
• Density-driven higher-order topological phase transitions in amorphous solids
• Chiral Majorana Hinge Modes in Superconducting Dirac Materials
• Dual Topological Insulator Device with Disorder Robustness
• Even-Odd Layer-Dependent Exchange Bias Effect in MnBi2Te4 Chern Insulator Devices
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• ${\mathbb{Z}}_2$ Spin Hopf Insulator: Helical Hinge States and Returning Thouless Pump
• Lattice distortion induced first and second order topological phase transition in rectangular high-T${}_{\mathrm{c}}$ superconducting monolayer
• A Dirac fermion model associated with second order topological insulator
• Weyl-like points from band inversions of spin-polarised surface states in NbGeSb
• Computing observables without eigenstates: applications to Bloch Hamiltonians
• Emerging topological bound states in Haldane model zigzag nanoribbons
• Impurity bound states as detectors of topological band structures revisited
• Topological hinge modes in Dirac semimetals
• Crystalline Responses for Rotation-Invariant Higher-Order Topological Insulators
• Building programable integrated circuits through disordered Chern insulators
• Robustness of Helical Hinge States of Weak Second-Order Topological Insulators
• Dynamical Piezomagnetic Effect in Time-Reversal Invariant Weyl Semimetals with Axionic Charge-Density Waves
• Lecture Notes on Topological Crystalline Insulators
• Higher-Order Topological Mott Insulator on the Pyrochlore Lattice
• Single-mode lasing based on PT-breaking of two-dimensional photonic higher-order topological insulator
• Competition of non-Hermitian skin effect and topological localization of corner states observed in circuits
• Topological properties of two-dimensional photonic square lattice without $C_4$ and $M_{x(y)}$ symmetries
• Phononic Stiefel-Whitney topology with corner vibrational modes in two-dimensional Xenes and ligand-functionalized derivatives
• Higher-order topological superconductors from Weyl semimetals
• Topological crystalline insulator state with type-II Dirac fermions in transition metal dipnictides
• Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant
• Boundary edge networks induced by bulk topology
• Higher-order Topological Phases of Magnons in van der Waals Honeycomb Ferromagnets
• Escape from black holes in materials: Type II Weyl semimetals and generic edge states
• Robustness of chiral edge modes in fractal-like-lattices below two dimensions: A case study
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
• Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians
• Second-Order Topological Insulator in van der Waals Heterostructures of CoBr${}_2$/Pt${}_2$HgSe${}_3$/CoBr${}_2$
• Second-Order Topological Insulator in Two-Dimensional C2N and Its Derivatives
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Hybrid-order topological odd-parity superconductors via Floquet engineering
• Topological states in a dimerized system with staggered magnetic fluxes
• Topological transitions and Anderson localization of light in disordered atomic arrays
• Two-dimensional weak-type topological insulators in inversion symmetric crystals
• Second-order topological modes in two-dimensional continuous media
• Hinge states in a system of coupled Rashba layers
• Quantized surface magnetism and higher-order topology: Application to the Hopf insulator
• Bulk and surface electronic structure of Bi${}_4$Te${}_3$ from $GW$ calculations and photoemission experiments
• Light bullets in Su-Schrieffer-Heeger photonic topological insulators
• Engineering topologically protected zero-dimensional interface end states in antiferromagnetic heterojunction graphene nanoflakes
• Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
• Toeplitz operators on concave corners and topologically protected corner states
• Entanglement in a second order topological insulator on a square lattice
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Sublattice-sensitive Majorana Modes
• Signatures of the Majorana spin in electrical transport through a Majorana nanowire
• Pressure-induced Superconductivity in Zintl Topological Insulator SrIn2As2
• Role of the edges in a quasicrystalline Haldane model
• Topological corner modes in a brick lattice with nonsymmorphic symmetry
• Higher-order topological heat conduction on a lattice for detection of corner states
• Majorana corner states on the dice lattice
• Floquet second-order topological Anderson insulator hosting corner localized modes
• Interaction-induced quantum spin Hall insulator in the organic Dirac electron system $\alpha$-(BEDT-TSeF)${}_2$I${}_3$
• Dephasing enhanced strong Majorana zero modes in 2D and 3D higher-order topological superconductors
• High-Order Topological Phase Diagram Revealed by Anomalous Nernst Effect in Janus ScClI Monolayer
• High-temperature Majorana corner modes in a $d+i{d}^{\prime }$ superconductor heterostructure: Application to twisted bilayer cuprate superconductors
• Photonic nodal lines with quadrupole Berry curvature distribution
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Mirror real Chern insulator in two and three dimensions
• The General Principle behind Magnetization-induced Second-Order Topological Corner States in the Kane-Mele Model
• Dynamically characterizing topological phases by high-order topological charges
• Pressure-induced superconductivity in weak topological insulator BiSe
• Theory of edge states based on the hermiticity of tight-binding Hamiltonian operators
• Multi-frequency optical lattice for dynamic lattice-geometry control
• Topological phases of the dimerized Hofstadter butterfly
• Correlation Effects in Quadrupole Insulators: a Quantum Monte Carlo Study
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Magnetic Flux Periodicity in Second Order Topological Superconductors
• Topological nature of higher-order hinge states revealed by spin transport
• Quantized charge-pumping in higher-order topological insulators
• Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Long-lived Andreev states as evidence for protected hinge modes in a bismuth nanoring Josephson junction
• Effects of Disorder On Thouless Pumping In Higher-Order Topological Insulators
• Classification and construction of interacting fractonic higher-order topological phases
• Transparent Josephson Junctions in Higher-Order Topological Insulator WTe2 via Pd Diffusion
• Classification of three-photon states in waveguide quantum electrodynamics
• Topological crystalline insulators from stacked graphene layers
• Group theory study of the vibrational modes and magnetic order in the topological antiferromagnet MnBi${}_2$Te${}_4$
• Light-induced charge and spin Hall currents in materials with $C_{4}K$ symmetry
• Effective field theories of topological crystalline insulators and topological crystals
• Dirac cones and higher-order topology in quasi-continuous media
• Topological d-wave superconductivity in two dimensions
• Observation of gapless corner modes in synthetic translation dimensions
• Orbital shift-induced boundary obstructed topological materials with a large energy gap
• Effective action approach to the filling anomaly in crystalline topological matter
• Topological states on uneven (Pb,Sn)Se (001) surfaces
• Tailoring Quadrupole Topological Insulators with Periodic Driving and Disorder
• Transport Induced Dimer State from Topological Corner States
• Fractional hinge and corner charges in various crystal shapes with cubic symmetry
• Third-order topological insulator induced by disorder
• Observation of emergent Dirac physics at the surfaces of acoustic higher-order topological insulators
• Interlayer Coupling Induced Topological Phase Transition to Higher Order
• Inducing a many-body topological state of matter through Coulomb-engineered local interactions
• Persistence of Monoclinic Crystal Structure in Three-Dimensional Second-Order Topological Insulator Candidate 1T'-MoTe2 Thin Flake without Structural Phase transition
• Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
• Dynamical Detection of Topological Spectral Density
• Magnetic band representations, Fu-Kane-like symmetry indicators and magnetic topological materials
• Spin-orbit insulating phase in SnTe cubic nanowires: consequences on the topological surface states
• Thermodynamic transitions and topology of spin-triplet superconductivity: Application to UTe${}_2$
• Topological Corner States in Graphene by Bulk and Edge Engineering
• Topological and dynamical features of periodically driven spin ladders
• Zeros of Green Functions in Topological Insulators
• Solitonic in-gap modes in a superconductor-quantum antiferromagnet interface
• Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Quantum transport evidence of the boundary states and Lifshitz transition in Bi${}_4$Br${}_4$
• Topological Magnetoelectric Response in Ferromagnetic Axion Insulators
• Controlling the Deformation of Metamaterials: Corner Modes via Topology
• Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
• Real-space Obstruction in Quantum Spin Hall Insulators
• Higher-order Skin Effect through a Hermitian-non-Hermitian Correspondence and Its Observation in an Acoustic Kagome Lattice
• Aharonov-Bohm Effect in Three-dimensional Higher-order Topological Insulator
• Multiple higher-order topological phases with even and odd pairs of zero-energy corner modes in a $C_3$ symmetry broken model
• Weak antilocalization beyond the fully diffusive regime in Pb1-xSnxSe topological quantum wells
• Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
• Observation of the topological Dirac fermions and surface states in superconducting BaSn3
• Time-reversal invariant finite-size topology
• Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
• Linear Response in Topological Materials
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Topological BF description of 2D accelerated chiral edge modes
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Two-Dimensional Higher-Order Topological Metals
• Network model for higher-order topological phases
• Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines
• Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation
• Rotational symmetry breaking and partial Majorana corner states in a high-Tc superconductor based heterostructure
• Universal Higher-Order Topology from 5D Weyl semimetal: Edge topology, edge Hamiltonian and nested Wilson loop
• Abundance of second order topology in $C_3$ symmetric two-dimensional insulators
• Revisiting (higher order and crystalline) topology in old models of lead telluride
• Nonlinear Corner States in Topologically Nontrivial Kagome Lattice
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Topologically Protected Edge States in Triangular Lattices
• Third-order topological insulator in three-dimensional lattice of magnetic vortices
• Out of equilibrium chiral higher order topological insulator on a $\pi$-flux square lattice
• Simulating Floquet topological phases in static systems
• Observation of nonlinear topological corner states originating from different spectral charges
• Atoms to topological electronic materials: A bedtime story for beginners
• Long-Time Magnetic Relaxation in Antiferromagnetic Topological Material EuCd${}_2$As${}_2$
• Discovery of Ĉ${}_2$ rotation anomaly in topological crystalline insulator SrPb
• Anomalous levitation and annihilation in Floquet topological insulators
• Floquet higher-order topological phases in momentum space
• Topological nodal chains in optical lattices
• Protected Gapless Edge States In Trivial Topology
• Multi-Dimensional Quantum Walks: a Playground of Dirac and Schrödinger Particles
• Higher-order topological insulator in a modified Haldane-Hubbard model
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Higher-order topological phase of interacting photon pairs
• Delocalization of edge states in topological phases
• Spin-polarization of topological crystalline and normal insulator Pb${}_{1-x}$Sn${}_x$Se (111) epilayers probed by photoelectron spectroscopy
• Topology and Magnetism in the Kondo Insulator Phase Diagram
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry
• Model Hamiltonian for Altermagnetic Topological Insulators
• Green's Function Approach to Interacting Higher-order Topological Insulators
• Persistence of symmetry-protected Dirac points at the surface of the topological crystalline insulator SnTe upon impurity doping
• Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model
• Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
• Wannier band transitions in disordered $\pi$-flux ladders
• Selectable diffusion direction with topologically protected edge modes
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Holstein polaron in a pseudospin-$1$ quantum spin Hall system: first and second order topological phase transitions
• Anisotropic positive linear and sub-linear magnetoresistivity in the cubic type-II Dirac metal Pd${}_3$In${}_7$
• Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions
• Multiorder topological superfluid phase transitions in a two-dimensional optical superlattice
• Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number
• AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
• Gapless higher-order topology and corner states in Floquet systems
• Multi higher-order Dirac and nodal line semimetals
• Crystalline-electromagnetic responses of higher order topological semimetals
• Exotic Invertible Phases with Higher-Group Symmetries
• 2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation
• Transport features of topological corner states in honeycomb lattice with multihollow structure
• Topological Wannier cycles for the bulk and edges
• Topologically localized insulators
• Engineering Topological Models with a General-Purpose Symmetry-to-Hamiltonian Approach
• Realizing Corner States in Artificial Crystals Based on Topological Spin Textures
• Higher-order topological corner states induced solely by onsite potentials with mirror symmetry
• Higher-order topological superconductivity in monolayer WTe${}_2$ from repulsive interactions
• Higher-order topological insulators in a crisscross antiferromagnetic model
• Multiplicative Majorana zero-modes
• Controllable Weyl Nodes and Fermi Arcs from Floquet Engineering Triple Fermions
• Axion insulators protected by C2T and their K-theory invariants and material realization
• Anomalous Crystal Shapes of Topological Crystalline Insulators
• Spin-Dependent High-Order Topological Insulator and Two Types of Distinct Corner Modes in Monolayer FeSe/GdClO Heterostructure
• Corner and Edge States in Topological Sierpinski Carpet Systems
• Competing topological phases in a non-Hermitian time-reversal symmetry-broken Bernevig-Hughes-Zhang model
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Topological Classical Systems with Generalized Chiral Symmetry
• Surface-dependent Majorana vortex phases in topological crystalline insulators
• Disorder-Induced Phase Transitions in Three-Dimensional Chiral Second-Order Topological Insulator
• Bulk-boundary-transport correspondence of the second-order topological insulators
• BerryEasy: A GPU enabled python package for diagnosis of nth-order and spin-resolved topology in the presence of fields and effects
• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence
• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
• Nodal lines and mapping to mirror Chern numbers in Ca${}_2$As family
• Unveiling Higher-Order Topology via Polarized Topological Charges
• The topological invariants of rotationally symmetric crystals
• Second-order topological insulator under strong magnetic field: Landau levels, Zeeman effect, and magnetotransport
• Gapless Fermionic Systems as Phase-space Topological Insulators: Non-perturbative Results from Anomalies
• Electric polarization and its quantization in one-dimensional non-Hermitian chains
• Microwave hinge states in a simple-cubic-lattice photonic crystal insulator
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Edge states mechanism for the anomalous quantum Hall effect in diatomic square lattice
• Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems
• Berezinskii-Kosterlitz-Thouless localization-localization transitions in disordered two-dimensional quantized quadrupole insulators
• Many-body multipole index and bulk-boundary correspondence
• Remote control of spin polarization of topological corner states
• Two-Dimensional Altermagnetic Iron Oxyhalides: Real Chern Topology and Valley-Spin-Lattice Coupling
• Topological Insulators with Hybrid-order Boundary States
• Extrinsic topology of Floquet anomalous boundary states in quantum walks
• Spin-Selective Second-Order Topological Insulators Enabling Cornertronics in 2D Altermagnets
• Stacking-Induced Symmetry-Protected Topological Phase Transitions
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Higher-order topology and corner triplon excitations in two-dimensional quantum spin-dimer models
• Topological quantum criticality from multiplicative topological phases
• Higher-order topology in twisted multilayer systems: a review
• Boundary obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field
• Ferroelectric polarization controlled orbital Hall conductivity in a higher-order topological insulator: \textit{d1T}-phase monolayer MoS${}_2$
• Nontrivial gapless electronic states at the stacking faults of weak topological insulators
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Discovery of topological metamaterials by symmetry relaxation and smooth topological indicators
• Second-order topological insulator in a coinless discrete-time quantum walk
• Generic Approach to Intrinsic Magnetic Second-order Topological Insulators via Inverted $p-d$ Orbitals
• Higher-order Topological States in Chiral Split Magnons of Honeycomb Altermagnets
• Structural, electronic and topological properties of 3D TmBi compound
• Emergent metallicity at the grain boundaries of higher-order topological insulators
• Fermionic tensor networks for higher order topological insulators from charge pumping
• XFe4Ge2 (X = Y, Lu) and Mn3Pt: Filling-enforced magnetic topological metals
• Fractional corner charges in threefold-symmetric two-dimensional materials with fragile topology
• STM observation of the hinge-states of bismuth nanocrystals
• Floquet Engineering of Lie Algebraic Quantum Systems
• Three-Dimensional Quantum Anomalous Hall Effect in Magnetic Topological Insulator Trilayers of Hundred-Nanometer Thickness
• Interaction-Driven Topological Switch in a $P$-Band Honeycomb Lattice
• Orbital Edelstein effect of electronic itinerant orbital motion at edges
• Catalyst-free MBE growth of PbSnTe nanowires with tunable aspect ratio
• Gapless Criterion for Crystals from Effective Axion Field
• Hierarchical Topological States in Thermal Diffusive Networks
• Engineering rich two-dimensional higher-order topological phases by flux and periodic driving
• Majorana modes in striped two-dimensional inhomogeneous topological superconductors
• Classification of topological invariants related to corner states
• Mod-two APS index and domain-wall fermion
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Light-Induced Mirror Symmetry Breaking and Charge Transport
• Chiral Hinge Transport in Disordered Non-Hermitian Second-Order Topological Insulators
• Magnetic impurities along the edge of a quantum spin Hall insulator: Realizing a one-dimensional AIII insulator
• Nonlinear control of photonic higher-order topological bound states in the continuum
• Unconventional hybrid-order topological insulators
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Two-dimensional orbital-obstructed insulators with higher-order band topology
• Higher-order topological superconductor phases in a multilayer system
• Topological reflection matrix
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• Corner states of two-dimensional second-order topological insulators with a chiral symmetry and broken time reversal and charge conjugation
• Distinguishing trivial and topological quadrupolar insulators by Wannier-Stark ladders
• Observation of nonlinear higher-order topological insulators with unconventional boundary truncations
• Topological physics in quantum critical systems
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Second-order topology and supersymmetry in two-dimensional topological insulators
• Tailoring higher-order topological phases via orbital hybridization
• Topological electronic structure of twin boundaries and twinning superlattices in the SnTe material class
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence
• Topological optical Raman superlattices
• Second Euler number in four dimensional synthetic matter
• Pentagonal nanowires from topological crystalline insulators: a platform for intrinsic core-shell nanowires and higher-order topology
• Topological Corner States in Bilayer and Trilayer Systems with Vertically Stacked Topological Heterostructures
• Majorana corner pairs in a two-dimensional $s$-wave cold atomic superfluid
• Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
• Inducing anisotropies in Dirac fermions by periodic driving
• Second-order topological insulator in periodically driven lattice
• Higher-order topological superconductors characterized by Fermi level crossings
• Topological characteristics of gap closing points in nonlinear Weyl semimetals
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Hybrid-Order Topological Phase And Transition in 1H Transition Metal Compounds
• Pumping with Symmetry
• Corner Modes and Ground-State Degeneracy in Models with Gauge-Like Subsystem Symmetries
• Exceptional second-order topological insulators
• Hinge States of Second-Order Topological Insulators as a Mach-Zehnder Interferometer
• Gate-tunable topological superconductivity in a supramolecular electron spin lattice
• An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped Invariants related to corner states
• Second-order topological insulator in Bilayer borophene
• Topological Signatures in Nodal Semimetals through Neutron Scattering
• Scattering theory of higher order topological phases
• Majorana corner states in square and Kagome quantum spin liquids
• In the Pursuit of Majorana Modes in Iron-based High-$T_c$ Superconductors
• General corner charge formulas in various tetrahedral and cubic space groups
• Time-reversal invariant topological skyrmion phases
• Axion insulator, Weyl points, quantum anomalous Hall effect and magnetic topological phase transition in Eu3In2As4
• Anomalous in-gap edge states in two-dimensional pseudospin-1 Dirac insulators
• Higher-order topology in honeycomb lattice with Y-Kekulé distortions
• Recipe for higher-order topology on the triangular lattice
• Disorder-induced phase transitions in double HgTe quantum wells
• Coexisting surface states in the weak and crystalline topological insulator Bi_2TeI
• Renormalization approach to the analysis and design of Hermitian and non-Hermitian interfaces
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Theoretical analysis of glide-Z_2 magnetic topological photonic crystals
• Boundary and defect criticality in topological insulators and superconductors
• Inexorable Edge Kondo Breakdown in Topological Kondo Insulators
• Optical Berry Curvature of Hinge State and Its Detection
• Ferromagnetic-electrodes-induced Hall effect in topological Dirac semimetals
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Fragmented exceptional points and their bulk and edge realizations in lattice models
• Revealing Higher-Order Topological Bulk-boundary Correspondence in Bismuth Crystal with Spin-helical Hinge State Loop and Proximity Superconductivity
• Mapping rules from nodal line semimetal to topological crystalline insulator in face centered cubic lattice
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants
• Intrinsic (Axion) Statistical Topological Insulator
• Topological parafermion corner states in clock-symmetric non-Hermitian second-order topological insulator
• Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator
• Fragile topology in nodal-line semimetal superconductors
• Theory of fractional corner charges in cylindrical crystal shapes
• Higher-Order Topological Systems and Their Sub-Symmetry-Protected Topology
• Altermagnetism and its induced higher-order topology on the Lieb lattice
• Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model
• Photonic quadrupole topological phases in zero-dimensional cavity with synthetic dimensions
• Dynamical characterization of topological phases beyond the minimal models
• Hermitian and non-Hermitian topology in active matter
• Realization of a three-dimensional quantum Hall effect in a Zeeman-induced second order topological insulator on a torus
• Mirror-symmetry protected higher-order topological zero-frequency boundary and corner modes in Maxwell lattices
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
• Higher order topological state induced by $d$-wave competing orders in high-T${}_c$ superconductor based heterostructure
• Hybrid symmetry class topological insulators
• Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides
• Anisotropic Penetration Depths of Corner States in a Higher-Order Topological Insulator
• Engineering Hierarchical Symmetries
• Unconventional Topological Insulators from Extended Topological Band Degeneracies
• Experimental Observation of Bound States of 2D Dirac Electrons at Surface Steps of the Topological Insulator Bi${}_2$Se${}_3$
• Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges
• Finite-temperature topological invariant for higher-order topological insulators
• Arboreal Obstructed Atomic Insulating and Metallic Phases of Fermions
• Quasiperiodic Quadrupole Insulators
• Topological defect-mediated corner states and higher-order bulk topology in a two-dimensional crystalline insulator
• Inducing ${\mathbb{Z}}_2$ Topology in Twisted Nodal Superconductors
• Quantum Coherent Transport of 1D ballistic states in second order topological insulator Bi${}_4$Br${}_4$
• Topological Aspects of Dirac Fermions in a Kagomé Lattice
• Topological Aspects of Antiferromagnets
• Physical rendering of synthetic spaces for topological sound transport
• C*-framework for higher-order bulk-boundary correspondences
• Observation of Square-Root Higher-Order Topological States in Photonic Waveguide Arrays
• Surface theory of a second-order topological insulator beyond the Dirac approximation
• Floquet-Anderson localization in the Thouless pump and how to avoid it
• Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
• Breakdown of boundary criticality and exotic topological semimetals in $\mathcal{P}\mathcal{T}$-invariant systems
• Spin separation and filtering assisted by topological corner states in the Kekulé lattice
• Multiple topological corner states in the continuum of extended kagome lattice
• Rotating Majorana Zero Modes in a disk geometry
• Chiral Majorana Edge Modes and Vortex Majorana Zero Modes in Superconducting Antiferromagnetic Topological Insulator
• Electronic band structure from quasiparticle interference and Landau quantization in WTe${}_2$
• Perfectly localized Majorana corner modes in fermionic lattices
• RKKY interaction in helical higher-order topological insulators
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Optically Controlled Topological Phases in the Deformed $\alpha -T_3$ Lattice
• Third-order Orbital Corner State and its Realization in Acoustic Crystals
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Many-Body Quadrupolar Sum Rule for Higher-Order Topological Insulator
• Asymmetric topological pumping in nonparaxial photonics
• Topological insulators and geometry of vector bundles
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Photonic Higher-Order Topological States Induced by Long Range Interactions
• Nonlinearity-induced corner states in a kagome lattice
• Network model for magnetic higher-order topological phases
• Artificial Gauge Field Engineered Excited-State Topology: Control of Dynamical Evolution of Localized Spinons
• Magnetic-flux tunable electronic transport through domain walls in a three-dimensional second-order topological insulator
• Higher-order topological insulators in two-dimensional antiferromagnetic and altermagnetic chromium-based group-IV chalcogenides
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Engineering Two-Dimensional Hybrid-Order Topological Insulators via Trilayer Coupling
• Understanding the index theorems with massive fermions
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Topological Properties of Bilayer $\alpha -T_3$ Lattice Induced by Polarized Light
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Dissipative Hot-spot Enabled Shock and Bounce Dynamics via Terahertz Quantum Quenches in Helical Edge States
• Higher-Order Topology in Monolayer FeSe
• Current switching behavior mediated via hinge modes in higher-order topological phases using altermagnets
• Hidden wallpaper fermion and third-order topological insulator
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges
• Symmetry-protected gates of Majorana qubits in a high-$T_c$ superconductor platform
• An exceptional surface and its topology
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Disclinations, dislocations, and emanant flux at Dirac criticality
• Unveiling Topological Hinge States in the Higher-Order Topological Insulator WTe${}_2$ Based on the Fractional Josephson Effect
• Theory of quantum spin-Hall topological lasers
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Dichotomy of flat bands in the van der Waals ferromagnet Fe${}_5$GeTe${}_2$
• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals
• The Quadrupole Moment of Higher-Order Topological Insulator at Finite temperature
• Extended Haldane model -- a modern gateway to topological insulators
• Topological Optical Pseudospin Injection Beyond Weyl Semimetals
• Intrinsic higher-order topological states in 2D honeycomb Z_2 quantum spin Hall insulators
• Fractional chiral second-order topological insulator from a three-dimensional array of coupled wires
• Higher order topology in a Creutz ladder
• Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet
• Topological photocurrent responses from chiral surface Fermi arcs
• Obstructed Atomic Insulators and Superfluids of Fermions Coupled to ${\mathbb{Z}}_2$ Gauge Fields
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Wilson Loop and Topological Properties in 3D Woodpile Photonic Crystal
• Corner Flat Bands Induced by $d$-Density Wave and Partial Corner State Modification Due to Competition with $d$-Wave Superconductivity
• Hinge modes of three-dimensional Euler insulators
• Boundary Condition Analysis of First and Second Order Topological Insulators
• Nanoimprinted topological laser in the visible
• Topological energy pumping in a quasi-periodically driven four-level system
• Multi-dimensional wave steering with higher-order topological phononic crystal
• Classification of topological insulators and superconductors with multiple order-two point group symmetries
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Robust zero-energy states in two-dimensional Su-Schrieffer-Heeger topological insulators
• Higher-order topological quantum paramagnets
• Graphyne as a second-order and real Chern topological insulator in two dimensions
• Nodal lines in a honeycomb plasmonic crystal with synthetic spin
• Floquet second-order topological insulator in strained graphene
• Dynamics of 2D topological quadrupole insulator and Chern insulator induced by real-space topological changes
• Phonons Drive the Topological Phase Transition in Quasi-One-Dimensional Bi${}_4$I${}_4$
• Higher-order Quantum Spin Hall Effect of Light
• Magnetically tunable Dirac and Weyl fermions in the Zintl materials family
• Higher-order topological phases protected by noninvertible and subsystem symmetries
• Second-order topological insulator induced by compensated altermagnetism without bulk spin splitting
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
• Valley- and Orbital-Controlled 2D Chern Insulators Without Spin-orbit Interaction
• Direct visualization of topological transitions and higher-order topological states in photonic metasurfaces
• Semimetals without correspondence between the topological charge of nodal line/surface and Fermi arc
• Non-Hermitian Higher-Order Dirac Semimetals
• Non-Hermitian Higher-Order Weyl Semimetals
• Emergent One-Dimensional Helical Channel in Higher-Order Topological Insulators with Step Edges
• Tunable effective length of fractional Josephson junctions
• Topological Pseudospin Hall Effect and Multi-frequency Corner Modes in Kagome-based Lattices
• Gapless hinge states from adiabatic pumping of axion coupling
• Altermagnetism Induced Bogoliubov Fermi Surfaces Form Topological Superconductivity
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Non-Hermitian physics and topological phenomena in convective thermal metamaterials
• Hofstadter Butterflies in Topological Insulators
• Proposal for realizing and probing topological crystalline insulators in optical lattices
• Topological Photonics on a Small Scale
• Three-nodal surface phonons in solid-state materials: Theory and material realization
• Non-Hermitian second-order topological insulator with point gap
• Coupled-wire construction of non-Abelian higher-order topological phases
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn
• Type-II Weyl Excitation in Vortex Arrays
• Symmetry-protected topological wire in a topological vacuum
• Higher-order topological insulator in cubic semiconductor quantum wells
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries
• Dynamical Symmetry Indicators for Floquet Crystals
• When Wannier centers jump: Critical points between atomic insulating phases
• Three-dimensional higher-order topological insulator protected by cubic symmetry
• Emergence of Hermitian topology from non-Hermitian knots
• Anti-higher-order Weyl semimetal
• Weak ${\mathbb{Z}}_2$ Supertopology
• Layer-number parity induced topological phase transition