$(d-2)$-dimensional edge states of rotation symmetry protected topological states

Abstract

We study fourfold rotation invariant gapped topological systems with time-reversal symmetry in two and three dimensions ($d=2,3$). We show that in both cases nontrivial topology is manifested by the presence of the $(d-2)$-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wannier centers of filled bands, and can be readily calculated using a Fu-Kane-like formula when inversion symmetry is also present. The theory is extended to strongly interacting systems through explicit construction of microscopic models having robust $(d-2)$-dimensional edge states.

arXiv commentv5, accepted in prl, the explicit Z8 Fu-Kane-like formulas provided

References in corpus (25)

• Topological Insulators
• Topological insulators and superconductors
• Maximally-localized generalized Wannier functions for composite energy bands
• Topological Insulators in Three Dimensions
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Topological quantum chemistry
• Topological Crystalline Insulators in the SnTe Material Class
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Reflection symmetric second-order topological insulators and superconductors
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Braiding statistics approach to symmetry-protected topological phases
• Inversion Symmetric Topological Insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Wannier representation of Z_2 topological insulators
• 2D symmetry protected topological orders and their protected gapless edge excitations
• From Luttinger liquid to non-Abelian quantum Hall states
• Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology
• Boundary Green functions of topological insulators and superconductors
• Wire deconstructionism of two-dimensional topological phases
• Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires
• Quantum Spin Hall Effect in Strip of Stripes Model
• Integer and Fractional Quantum Anomalous Hall Effect in a Strip of Stripes Model

Cited by in corpus (658)

• Non-Hermitian Physics
• 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
• Reflection symmetric second-order topological insulators and superconductors
• 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
• 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
• Higher-order topological insulators and superconductors protected by inversion symmetry
• 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
• Observation of second-order topological insulators in sonic crystals
• 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
• Elastic higher-order topological insulator with topologically protected corner states
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Higher-order non-Hermitian skin effect
• 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
• Quantitative mappings between symmetry and topology in solids
• Topological Non-Hermitian skin effect
• 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
• 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
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Higher Order Topological Phases: A General Principle of Construction
• Observation of a higher-order topological bound state in the continuum
• Experimental Observation of Higher-Order Topological Anderson Insulators
• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Efficient Topological Materials Discovery Using Symmetry Indicators
• Weak-Pairing Higher Order Topological Superconductors
• Helical Topological Edge States in a Quadrupole Phase
• Majorana Kramers pairs in higher-order topological insulators
• Topological Materials Discovery from Crystal Symmetry
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Higher-Order Weyl Semimetals
• Non-linear second-order topological insulators
• 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
• 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
• 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
• Bound states in the continuum of higher-order topological insulators
• 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 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
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Rotation Anomaly and Topological Crystalline Insulators
• Liganded Xene as a Prototype of Two-Dimensional Stiefel-Whitney Insulators
• 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
• Lattice models with exactly solvable topological hinge and corner states
• Floquet second-order topological insulators from nonsymmorphic space-time symmetries
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Higher-order topological insulators in amorphous solids
• Many-Body Order Parameters for Multipoles in Solids
• Quadrupole Topological Photonic Crystals
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
• Boundary-obstructed topological phases
• 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
• 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
• Symmetry-protected hierarchy of anomalous multipole topological band gaps in nonsymmorphic metacrystals
• Non-Hermitian second-order skin and topological modes
• Realization of the square-root higher-order topological insulator in electric circuits
• Second-order Topological Superconductors with Mixed Pairing
• Hybrid-order topological insulators in a phononic crystal
• Magnetic second-order topological insulators and semimetals
• Tutorial: Computing topological invariants in two-dimensional photonic crystals
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Emergent Phases of Fractonic Matter
• 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
• Higher-order photonic topological states in surface-wave photonic crystals
• 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
• Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials
• Diagnosis for topological semimetals in the absence of spin-orbital coupling
• 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
• Higher-order topological phases in tunable $C_3$-symmetric photonic crystals
• Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Hofstadter Topology: Non-crystalline Topological Materials at High Flux
• Topological states from topological crystals
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne
• Engineering Fragile Topology in Photonic Crystals: Topological Quantum Chemistry of Light
• Generating a second-order topological insulator with multiple corner states by periodic driving
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Structural Disorder Induced Second-order Topological Insulators in Three Dimensions
• Proximity-induced Majorana hinge modes in antiferromagnetic topological insulators
• Unified understanding of symmetry indicators for all internal symmetry classes
• Square-root higher-order topological insulator on a decorated honeycomb lattice
• Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics
• Topological states on fractal lattices
• Higher-order Dirac sonic crystals
• Creation and Manipulation of Higher-Order Topological States by Altermagnets
• MagneticTB: A package for tight-binding model of magnetic and non-magnetic materials
• Coupling between Exciton-Polariton Corner Modes through Edge States
• Gapped Topological Kink States and Topological Corner States in Graphene
• On-chip higher-order topological micromechanical metamaterials
• Evidence for Higher order topology in Bi and Bi${}_{0.92}$Sb${}_{0.08}$
• Higher-order topological superconductors in $\mathcal{P}$-, $\mathcal{T}$-odd quadrupolar Dirac materials
• Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons
• Braiding Majorana corner modes in a second-order topological superconductor
• 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
• Nonlinearity induced topological physics in momentum space and real space
• Four-Dimensional Higher-Order Chern Insulator and Its Acoustic Realization
• Nonlinear imaging of nanoscale topological corner states
• Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Topolectrical-circuit realization of 4D hexadecapole insulator
• 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
• Sub-symmetry protected topological states
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Quantum Metric and Correlated States in Two-dimensional Systems
• General corner charge formula in two-dimensional C_n-symmetric higher-order topological insulators
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Boundary-obstructed topological high-T${}_c$ superconductivity in iron pnictides
• Experimental identification of the second-order non-Hermitian skin effect with physics-graph-informed machine learning
• Measurement-only quantum computation with Majorana corner modes
• Phase tunable second-order topological superconductor
• Higher-Order Topological Dirac Superconductors
• Floquet generation of Second Order Topological Superconductor
• 3D hinge transport in acoustic higher-order topological insulators
• Higher-Order Weyl-Exceptional-Ring Semimetals
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• Fragile Phases As Affine Monoids: Classification and Material Examples
• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
• All-electrically tunable networks of Majorana bound states
• Difficulties in operator-based formulation of the bulk quadrupole moment
• Twisted quadrupole topological photonic crystals
• Symmetry indicators of band topology
• Local invariants identify topology in metals and gapless systems
• 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
• Catalogue of topological phonon materials
• Evidence for Helical Hinge Zero Modes in an Fe-Based Superconductor
• Partial lattice defects in higher order topological insulators
• Fractional Topological Superconductivity and Parafermion Corner States
• Higher-order topological band structures
• Floquet Second-Order Topological Superconductor Driven via Ferromagnetic Resonance
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• Floquet higher-order topological insulators and superconductors with space-time symmetries
• Inverse design of higher-order photonic topological insulators
• Observation of symmetry protected zero modes in topolectrical circuits
• Higher-order topological superconductivity: possible realization in Fermi gases and Sr${}_2$RuO${}_4$
• Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators
• Floquet second-order topological insulators in non-Hermitian systems
• Topological Phases of Photonic Crystals under Crystalline Symmetries
• Effective Model for Fractional Topological Corner Modes in Quasicrystals
• Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• Nonlinear non-Hermitian higher-order topological laser
• Three-dimensional superconductors with hybrid higher order topology
• Quadrupole topological insulators in Ta2M3Te5 (M= Ni, Pd) monolayers
• Hierarchy of higher-order topological superconductors in three dimensions
• Kekule Lattice in Graphdiyne: Coexistence of Phononic and Electronic Higher-Order Band Topology
• Theory of Topological Corner State Laser in Kagome Waveguide Arrays
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Topological classification and diagnosis in magnetically ordered electronic materials
• Majorana bound states in semiconducting nanostructures
• Temperature Dependent Electronic Structure in a Higher Order Topological Insulator Candidate EuIn${}_2$As${}_2$
• Quantization in chiral higher order topological insulators: circular dichroism and local Chern marker
• Splitting the hinge mode of higher-order topological insulators
• Purely rotational symmetry-protected topological crystalline insulator $\alpha$-Bi4Br4
• Dislocation as a bulk probe of higher-order topological insulators
• Higher order topological superconductors as generators of quantum codes
• Simple model for second-order topological insulators and loop-nodal semimetals in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Topological Phases in Magnonics
• Strong and weak second-order topological insulators with hexagonal symmetry and ${\mathbb{Z}}_3$ index
• Plasmon-polaritonic quadrupole topological insulators
• Higher-order topological insulators in hyperbolic lattices
• Symmetry indicators for topological superconductors
• 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
• 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
• Bulk-corner correspondence of time-reversal symmetric insulators: deduplicating real-space invariants
• Inversion-symmetry protected chiral hinge states in stacks of doped quantum Hall layers
• Majorana Corner Modes in a Second-Order Kitaev Spin Liquid
• 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
• 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
• On the topological immunity of corner states in two-dimensional crystalline insulators
• Phononic real Chern insulator with protected corner modes in graphynes
• Corner states and topological transitions in two-dimensional higher-order topological sonic crystals with inversion symmetry
• Higher Order Bosonic Topological Phases in Spin Models
• Exact Higher-order Bulk-boundary Correspondence of Corner-localized States
• Higher-order topological pumping and its observation in photonic lattices
• `Unhinging' the surfaces of higher-order topological insulators and superconductors
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Higher-order Topological Hyperbolic Lattices
• Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices
• Reentrant localization transition in the Su-Schrieffer-Heeger model with random-dimer disorder
• Detection of second-order topological superconductors by Josephson junctions
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Corner charge and bulk multipole moment in periodic systems
• Helical Liquids in Semiconductors
• Time-induced second-order topological superconductors
• Weyl nodes with higher-order topology in an optically driven nodal-line semimetal
• Type-II quadrupole topological insulators
• Simulation of Higher-Order Topological Phases and Related Topological Phase Transitions in a Superconducting Qubit
• First and Second Order Topological Phases on Ferromagnetic Breathing Kagome Lattice
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system
• Higher-order topology in monolayer graphene
• Chiral Hinge Magnons in Second-Order Topological Magnon Insulators
• Non-Abelian Bloch oscillations in higher-order topological insulators
• Experimental observation of non-Hermitian higher-order skin interface states in topological electric circuits
• Entanglement polarization for the topological quadrupole phase
• Pfaffian formalism for higher-order topological insulators
• Demonstration of acoustic high-order Stiefel-Whitney semimetal in bilayer graphene sonic crystals
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Majorana and parafermion corner states from two coupled sheets of bilayer graphene
• Floquet Weyl semimetal phases in light-irradiated higher-order topological Dirac semimetals
• Edge-Corner Correspondence: Boundary-Obstructed Topological Phases with Chiral Symmetry
• Acoustic corner states in topological insulators with built-in Zeeman-like fields
• Realization of Surface-Obstructed Topological Insulators
• Fractional charge bound to a vortex in two dimensional topological crystalline insulators
• Topological States in Generalized Electric Quadrupole Insulators
• Two-dimensional topological materials discovery by symmetry-indicator method
• Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekulé Distortion
• Anomalous Quadrupole Topological Insulators in 2D Nonsymmorphic Sonic Crystals
• Pairing Obstructions in Topological Superconductors
• Higher-order topological superconductors based on weak topological insulators
• 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
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Fragile topologically flat band in the checkerboard antiferromagnetic monolayer FeSe
• Systematic generation of the cascade of anomalous dynamical first and higher-order modes in Floquet topological insulators
• Axion coupling in the hybrid Wannier representation
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• Higher-order topological Anderson insulators in quasicrystals
• High-throughput Investigations of Topological and Nodal Superconductors
• Discovery of Higher-Order Topological Insulators using the Spin Hall Conductivity as a Topology Signature
• Local markers for crystalline topology
• Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators
• Topological Superconductivity in an s-wave Superconductor and Its Implication to Iron-based Superconductors
• Disorder-Induced Quantum Phase Transitions in Three-Dimensional Second-Order Topological Insulators
• Topological crystalline insulator states in the Ca${}_2$As family
• Cornertronics in Two-Dimensional Second-Order Topological Insulators
• Delocalization Transition of Disordered Axion Insulator
• Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians
• Higher-order Fabry-Pérot Interferometer from Topological Hinge States
• Coulomb instabilities of 3D higher-order topological insulators
• Dirac States in an Inclined Two-Dimensional Su-Schrieffer-Heeger Model
• Two-particle Berry phase mechanism for Dirac and Majorana Kramers pairs of corner modes
• Geometric orbital magnetization in adiabatic processes
• Tunable Majorana corner modes in noncentrosymmetric superconductors: Tunneling spectroscopy and edge imperfections
• General corner states in 2D SSH model with intracelluar next-nearest-neighbour hopping
• Buckled honeycomb group-$V$--$S_6$ symmetric $(d-2)$ higher order topological insulators
• Higher-order topological insulators in antiperovskites
• Classification of Dirac points with higher-order Fermi arcs
• Piezoelectricity and Topological Quantum Phase Transitions in Two-Dimensional Spin-Orbit Coupled Crystals with Time-Reversal Symmetry
• Transition from metal to higher-order topological insulator driven by random flux
• Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
• Rotation Symmetry-Protected Topological Phases of Fermions
• Classification of crystalline insulators without symmetry indicators: atomic and fragile topological phases in twofold rotation symmetric systems
• Discovery of a hybrid topological quantum state in an elemental solid
• Anti-chiral edge states and hinge states based on the Haldane model
• Second-order topological insulator in breathing square lattice of magnetic vortices
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
• Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces
• Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
• Extended Bloch theorem for topological lattice models with open boundaries
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Higher-order valley vortices enabled by synchronized rotation in a photonic crystal
• Quantum dynamical characterization and simulation of topological phases with high-order band inversion surfaces
• Higher-order topological insulators in a magnetic field
• Higher-form Gauge Symmetries in Multipole Topological Phases
• Dynamical construction of Quadrupolar and Octupolar topological superconductors
• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors
• Hinge solitons in three-dimensional second-order topological insulators
• Edge states, corner states, and flat bands in a two-dimensional $\mathcal{P}\mathcal{T}$ symmetric system
• Interaction driven surface Chern insulator in nodal line semimetals
• Fractional Corner Charge of Sodium Chloride
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence
• Engineering exotic second-order topological semimetals by periodic driving
• Flat bands and higher-order topology in polymerized triptycene: Tight-binding analysis on decorated star lattices
• Boundaries of boundaries: a systematic approach to lattice models with solvable boundary states of arbitrary codimension
• Calculated magnetic exchange interactions in Dirac magnon material Cu3TeO6
• Wannier-type photonic higher-order topological corner states induced solely by gain and loss
• Appearance of hinge states in second-order topological insulators via the cutting procedure
• Theory of inversion-${\mathbb{Z}}_4$ protected topological chiral hinge states and its applications to layered antiferromagnets
• Symmetry-enforced Band Nodes in 230 Space Groups
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Topological excitonic corner states and nodal phase in bilayer quantum spin Hall insulators
• Hinged Quantum Spin-Hall Effect in Antiferromagnetic Topological Insulators
• Existence of Corner Modes in Elastic Twisted Kagome Lattices
• Hidden Breathing Kagome Topology in Hexagonal Transition Metal Dichalcogenides
• Quadrupole moments, edge polarizations, and corner charges in the Wannier representation
• Higher-order topological spin Hall effect of sound
• The hybrid-order topology of weak topological insulators
• Embedded Topological Insulators
• Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Magnon corner states in twisted bilayer honeycomb magnets
• Quadrupole spin polarization as signature of second-order topological superconductors
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• Edge states and corner modes in second-order topological phononic crystal plates
• Fractional Chiral Hinge Insulator
• Second-order topological corner states in zigzag graphene nanoflake with different types of edge magnetic configurations
• Higher-Order Topological Crystalline Insulating Phase and Quantized Hinge Charge in Topological Electride Apatite
• Generation of higher-order topological insulators using periodic driving
• Obstructed insulators and flat bands in topological phase-change materials
• Observation of backscattering induced by magnetism in a topological edge state
• Klein-bottle quadrupole insulators and Dirac semimetals
• Thermodynamic approach to electric quadrupole moments
• Engineering second-order topological insulators via coupling two first-order topological insulators
• Second-order and real Chern topological insulator in twisted bilayer $\alpha$-graphyne
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Non-Compact Atomic Insulators
• Unified characterization for higher-order topological phase transitions
• Strain engineered higher order topological phases for spin-3/2 Luttinger fermions
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Multidimensional sound propagation in 3D high-order topological sonic insulator
• Quasicrystalline second-order topological semimetals
• Three-dimensional topological semimetal phase in layered TaNiTe5 probed by de Haas-van Alphen effect
• Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Topological edge and corner states and fractional corner charges in blue phosphorene
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
• Constructing higher-order topological states in higher dimension
• Multiorbital edge and corner states in black phosphorene
• The Bulk-Hinge Correspondence and Three-Dimensional Quantum Anomalous Hall Effect in Second Order Topological Insulators
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Topological Crystalline Insulators with $C_2$ Rotation Anomaly
• Density-driven higher-order topological phase transitions in amorphous solids
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Universal Relation among Many-Body Chern Number, Rotation Symmetry, and Filling
• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals
• Topological Superconductivity from Unconventional Band Degeneracy with Conventional Pairing
• Weyl-like points from band inversions of spin-polarised surface states in NbGeSb
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• Robustness of Helical Hinge States of Weak Second-Order Topological Insulators
• Crystalline Responses for Rotation-Invariant Higher-Order Topological Insulators
• 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
• Double Majorana vortex zero modes in superconducting topological crystalline insulators with surface rotation anomaly
• Topological hinge modes in Dirac semimetals
• Higher-order Topological Phases of Magnons in van der Waals Honeycomb Ferromagnets
• Topological States in Two-Dimensional Su-Schrieffer-Heeger Models
• Phononic Stiefel-Whitney topology with corner vibrational modes in two-dimensional Xenes and ligand-functionalized derivatives
• Higher-order topological superconductors from Weyl semimetals
• Boundary edge networks induced by bulk topology
• Topological crystalline insulator state with type-II Dirac fermions in transition metal dipnictides
• Higher-Order Topological Mott Insulator on the Pyrochlore Lattice
• Competition of non-Hermitian skin effect and topological localization of corner states observed in circuits
• Second-Order Topological Insulator in van der Waals Heterostructures of CoBr${}_2$/Pt${}_2$HgSe${}_3$/CoBr${}_2$
• Hinge states in a system of coupled Rashba layers
• Topological states in a dimerized system with staggered magnetic fluxes
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Second-Order Topological Insulator in Two-Dimensional C2N and Its Derivatives
• Two-dimensional weak-type topological insulators in inversion symmetric crystals
• Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
• Hybrid-order topological odd-parity superconductors via Floquet engineering
• Majorana corner states on the dice lattice
• Spectroscopic signature of obstructed surface states in SrIn${}_2$P${}_2$
• Light bullets in Su-Schrieffer-Heeger photonic topological insulators
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Engineering topologically protected zero-dimensional interface end states in antiferromagnetic heterojunction graphene nanoflakes
• Sublattice-sensitive Majorana Modes
• Entanglement in a second order topological insulator on a square lattice
• High-temperature Majorana corner modes in a $d+i{d}^{\prime }$ superconductor heterostructure: Application to twisted bilayer cuprate superconductors
• Dephasing enhanced strong Majorana zero modes in 2D and 3D higher-order topological superconductors
• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Correlation Effects in Quadrupole Insulators: a Quantum Monte Carlo Study
• The General Principle behind Magnetization-induced Second-Order Topological Corner States in the Kane-Mele Model
• Topological phases of the dimerized Hofstadter butterfly
• Floquet second-order topological Anderson insulator hosting corner localized modes
• Long-lived Andreev states as evidence for protected hinge modes in a bismuth nanoring Josephson junction
• Magnetic Flux Periodicity in Second Order Topological Superconductors
• Effects of Disorder On Thouless Pumping In Higher-Order Topological Insulators
• Higher order topological matter and fractional chiral states
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Symmetry indicators in commensurate magnetic flux
• Topological nature of higher-order hinge states revealed by spin transport
• Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry
• Observation of emergent Dirac physics at the surfaces of acoustic higher-order topological insulators
• 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
• Interlayer Coupling Induced Topological Phase Transition to Higher Order
• Topological classification of intrinsic 3D superconductors using anomalous surface construction
• Transport Induced Dimer State from Topological Corner States
• Fractional hinge and corner charges in various crystal shapes with cubic symmetry
• A General Method to Design Acoustic Higher-Order Topological Insulators
• Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
• Topological Dipole Conserving Insulators and Multipolar Responses
• Dynamical Detection of Topological Spectral Density
• Topological Edge and Corner States in Biphenylene Network
• Real-space Obstruction in Quantum Spin Hall Insulators
• Aharonov-Bohm Effect in Three-dimensional Higher-order Topological Insulator
• Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
• Topological and dynamical features of periodically driven spin ladders
• Controlling the Deformation of Metamaterials: Corner Modes via Topology
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Thermodynamic electric quadrupole moments of nematic phases from first-principles calculation
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Network model for higher-order topological phases
• Rotational symmetry breaking and partial Majorana corner states in a high-Tc superconductor based heterostructure
• Abundance of second order topology in $C_3$ symmetric two-dimensional insulators
• Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation
• Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
• Universal quantum Fisher information and simultaneous occurrence of Landau-class and topological-class transitions in non-Hermitian Jaynes-Cummings models
• Out of equilibrium chiral higher order topological insulator on a $\pi$-flux square lattice
• Observation of nonlinear topological corner states originating from different spectral charges
• Hybrid-order topology in unconventional magnets of Eu-based Zintl compounds with surface-dependent quantum geometry
• Magnetic field filtering of the hinge supercurrent in unconventional metal NiTe${}_2$-based Josephson junctions
• Symmetry-Protected Topological Phase for Spin-Tensor-Momentum-Coupled Ultracold Atoms
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Revisiting (higher order and crystalline) topology in old models of lead telluride
• Third-order topological insulator in three-dimensional lattice of magnetic vortices
• Protected Gapless Edge States In Trivial Topology
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Green's Function Approach to Interacting Higher-order Topological Insulators
• Pseudo topological insulators
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry
• Quasi-One-Dimensional Higher-Order Topological Insulators
• Discovery of Ĉ${}_2$ rotation anomaly in topological crystalline insulator SrPb
• Multi-Dimensional Quantum Walks: a Playground of Dirac and Schrödinger Particles
• Floquet higher-order topological phases in momentum space
• Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model
• Entanglement Signature of Hinge Arcs, Fermi Arcs, and Crystalline Symmetry Protection in Higher-Order Weyl Semimetals
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Higher-order topological insulators in a crisscross antiferromagnetic model
• AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
• Crystalline-electromagnetic responses of higher order topological semimetals
• Robust Bulk States
• Topological Wannier cycles for the bulk and edges
• Topologically localized insulators
• Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number
• Multi higher-order Dirac and nodal line semimetals
• Higher-order topological corner states induced solely by onsite potentials with mirror symmetry
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Gapless higher-order topology and corner states in Floquet systems
• Realizing Corner States in Artificial Crystals Based on Topological Spin Textures
• Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions
• Topological Classical Systems with Generalized Chiral Symmetry
• Two-Dimensional Altermagnetic Iron Oxyhalides: Real Chern Topology and Valley-Spin-Lattice Coupling
• Controlling Majorana modes by $p$-wave pairing in two-dimensional $p+id$ topological superconductors
• Spin-Dependent High-Order Topological Insulator and Two Types of Distinct Corner Modes in Monolayer FeSe/GdClO Heterostructure
• Many-body multipole index and bulk-boundary correspondence
• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence
• Disorder-Induced Phase Transitions in Three-Dimensional Chiral Second-Order Topological Insulator
• Extrinsic topology of Floquet anomalous boundary states in quantum walks
• Second-order topological insulator under strong magnetic field: Landau levels, Zeeman effect, and magnetotransport
• Fractal Surface States in Three-Dimensional Topological Quasicrystals
• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Competing topological phases in a non-Hermitian time-reversal symmetry-broken Bernevig-Hughes-Zhang model
• Topological Insulators with Hybrid-order Boundary States
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Observation of floating surface state in obstructed atomic insulator candidate NiP${}_2$
• Bulk-boundary-transport correspondence of the second-order topological insulators
• Remote control of spin polarization of topological corner states
• Interaction-Driven Topological Switch in a $P$-Band Honeycomb Lattice
• Emergent metallicity at the grain boundaries of higher-order topological insulators
• Higher-order topology in twisted multilayer systems: a review
• Generic Approach to Intrinsic Magnetic Second-order Topological Insulators via Inverted $p-d$ Orbitals
• Takagi topological insulator with odd $\mathcal{P}\mathcal{T}$ pairs of corner states
• XFe4Ge2 (X = Y, Lu) and Mn3Pt: Filling-enforced magnetic topological metals
• Second-order topological insulator in a coinless discrete-time quantum walk
• Hierarchical Topological States in Thermal Diffusive Networks
• STM observation of the hinge-states of bismuth nanocrystals
• Engineering rich two-dimensional higher-order topological phases by flux and periodic driving
• Second-order topology and supersymmetry in two-dimensional topological insulators
• Higher-order topological superconductor phases in a multilayer system
• Unconventional hybrid-order topological insulators
• 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
• Orbital Hall effect and topology on a two-dimensional triangular lattice: from bulk to edge
• Majorana corner pairs in a two-dimensional $s$-wave cold atomic superfluid
• Topologically compatible non-Hermitian skin effect
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Corner states of two-dimensional second-order topological insulators with a chiral symmetry and broken time reversal and charge conjugation
• Generalization of the Nested Wilson Loop Formalism in Topological Dirac Semimetals with Higher-order Fermi Arcs
• 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
• Zero-Energy State Localized near an Arbitrary Edge in Quadrupole Topological Insulators
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• A topological current divider
• Second-order topological insulator in Bilayer borophene
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Optical Berry Curvature of Hinge State and Its Detection
• Hinge States of Second-Order Topological Insulators as a Mach-Zehnder Interferometer
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• General corner charge formulas in various tetrahedral and cubic space groups
• Recipe for higher-order topology on the triangular lattice
• Exceptional second-order topological insulators
• Topological characteristics of gap closing points in nonlinear Weyl semimetals
• Axion insulator, Weyl points, quantum anomalous Hall effect and magnetic topological phase transition in Eu3In2As4
• Higher-order topology in honeycomb lattice with Y-Kekulé distortions
• Second-order topological insulator in periodically driven lattice
• Theoretical analysis of glide-Z_2 magnetic topological photonic crystals
• Majorana corner states in square and Kagome quantum spin liquids
• Anomalous in-gap edge states in two-dimensional pseudospin-1 Dirac insulators
• Higher-order topological superconductors characterized by Fermi level crossings
• Realization of a three-dimensional quantum Hall effect in a Zeeman-induced second order topological insulator on a torus
• Intertwined topological phases in TaAs2 nanowires with giant magnetoresistance and quantum coherent surface transport
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
• Unconventional Topological Insulators from Extended Topological Band Degeneracies
• Revealing Higher-Order Topological Bulk-boundary Correspondence in Bismuth Crystal with Spin-helical Hinge State Loop and Proximity Superconductivity
• Homotopy invariant in time-reversal and twofold rotation symmetric systems
• Topological parafermion corner states in clock-symmetric non-Hermitian second-order topological insulator
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Mixed-parity octupolar pairing and corner Majorana modes in three dimensions
• Cavity-induced topological edge and corner states
• Mirror-symmetry protected higher-order topological zero-frequency boundary and corner modes in Maxwell lattices
• Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices
• Higher order topological state induced by $d$-wave competing orders in high-T${}_c$ superconductor based heterostructure
• Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator
• Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges
• Theory of fractional corner charges in cylindrical crystal shapes
• Finite-temperature topological invariant for higher-order topological insulators
• Selective branching, quenching, and converting of topological modes
• Multi-locational Majorana Zero Modes
• Topological Aspects of Dirac Fermions in a Kagomé Lattice
• Third-order Orbital Corner State and its Realization in Acoustic Crystals
• Spin separation and filtering assisted by topological corner states in the Kekulé lattice
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Topological defect-mediated corner states and higher-order bulk topology in a two-dimensional crystalline insulator
• Chiral Majorana Edge Modes and Vortex Majorana Zero Modes in Superconducting Antiferromagnetic Topological Insulator
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Surface theory of a second-order topological insulator beyond the Dirac approximation
• Arboreal Obstructed Atomic Insulating and Metallic Phases of Fermions
• Floquet-Anderson localization in the Thouless pump and how to avoid it
• Observation of Square-Root Higher-Order Topological States in Photonic Waveguide Arrays
• Perfectly localized Majorana corner modes in fermionic lattices
• Second-order topological insulator and fragile topology in topological circuitry simulation
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Higher-order topological insulators in two-dimensional antiferromagnetic and altermagnetic chromium-based group-IV chalcogenides
• Network model for magnetic higher-order topological phases
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Engineering Two-Dimensional Hybrid-Order Topological Insulators via Trilayer Coupling
• 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
• Extended Haldane model -- a modern gateway to topological insulators
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Higher order topology in a Creutz ladder
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Higher-Order Topology in Monolayer FeSe
• Hidden wallpaper fermion and third-order topological insulator
• Current switching behavior mediated via hinge modes in higher-order topological phases using altermagnets
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Photonic Higher-Order Topological States Induced by Long Range Interactions
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Wilson Loop and Topological Properties in 3D Woodpile Photonic Crystal
• Obstructed Atomic Insulators and Superfluids of Fermions Coupled to ${\mathbb{Z}}_2$ Gauge Fields
• The Quadrupole Moment of Higher-Order Topological Insulator at Finite temperature
• Symmetry-protected gates of Majorana qubits in a high-$T_c$ superconductor platform
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Magnetic-flux tunable electronic transport through domain walls in a three-dimensional second-order topological insulator
• Topological Photonics on a Small Scale
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Graphyne as a second-order and real Chern topological insulator in two dimensions
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
• Classification of topological insulators and superconductors with multiple order-two point group symmetries
• Realization of second-order photonic square-root topological insulators
• Higher-order topological insulator in cubic semiconductor quantum wells
• Dynamical Symmetry Indicators for Floquet Crystals
• Emergent One-Dimensional Helical Channel in Higher-Order Topological Insulators with Step Edges
• Proposal for realizing and probing topological crystalline insulators in optical lattices
• Coupled-wire construction of non-Abelian higher-order topological phases
• Floquet second-order topological insulator in strained graphene
• Hofstadter Butterflies in Topological Insulators
• Hinge modes of three-dimensional Euler insulators
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn
• Corner Flat Bands Induced by $d$-Density Wave and Partial Corner State Modification Due to Competition with $d$-Wave Superconductivity
• Floquet first- and higher-order topological superconductors: A review
• Robust zero-energy states in two-dimensional Su-Schrieffer-Heeger topological insulators
• Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values
• Nanoimprinted topological laser in the visible
• Deconfined Quantum Phase Transition of a Higher-Order Symmetry-Protected Topological State
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Higher-order topological phases protected by noninvertible and subsystem symmetries
• Pseudospin-valley-coupled phononic topological insulator with edge and corner states
• Non-Hermitian Higher-Order Dirac Semimetals
• Non-Hermitian Higher-Order Weyl Semimetals
• Topological energy pumping in a quasi-periodically driven four-level system
• Boundary Condition Analysis of First and Second Order Topological Insulators