Topological insulators and superconductors: ten-fold way and dimensional hierarchy

Abstract

It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on the case, by a Z or a Z_2 topological invariant. This is an exhaustive classification. Here we construct representatives of topological insulators and superconductors for all five classes and in arbitrary spatial dimension d, in terms of Dirac Hamiltonians. Using these representatives we demonstrate how topological insulators (superconductors) in different dimensions and different classes can be related via dimensional reduction by compactifying one or more spatial dimensions (in Kaluza-Klein-like fashion). For Z-topological insulators (superconductors) this proceeds by descending by one dimension at a time into a different class. The Z_2-topological insulators (superconductors), on the other hand, are shown to be lower-dimensional descendants of parent Z-topological insulators in the same class, from which they inherit their topological properties. The 8-fold periodicity in dimension d that exists for topological insulators (superconductors) with Hamiltonians satisfying at least one reality condition (arising from time-reversal or charge-conjugation/particle-hole symmetries) is a reflection of the 8-fold periodicity of the spinor representations of the orthogonal groups SO(N) (a form of Bott periodicity). We derive a relation between the topological invariant that characterizes topological insulators/superconductors with chiral symmetry and the Chern-Simons invariant: it relates the invariant to the electric polarization (d=1), or to the magnetoelectric polarizability (d=3). Finally, we discuss topological field theories describing the space time theory of linear responses, and study how the presence of inversion symmetry modifies the classification.

66 pages, 5 figures, updated version of manuscript to appear in New Journal of Physics (copy of proofs submitted to Journal on May 12, 2010)

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• Two-dimensional Shiba lattices as possible platform for crystalline topological superconductivity
• Floquet Weyl Phases in a Three Dimensional Network Model
• Quantum Simulation of a Topological Mott Insulator with Rydberg Atoms in a Lieb Lattice
• Symmetry-protected topological phases in lattice gauge theories: topological QED${}_2$
• Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
• Non-Hermiticity and topological invariants of magnon Bogoliubov-de Gennes systems
• Topology and Observables of the Non-Hermitian Chern Insulator
• Particle-Hole Symmetries in Condensed Matter
• Revealing a topological connection between stabilities of Fermi surfaces and topological insulators/superconductors
• Atiyah-Hirzebruch Spectral Sequence in Band Topology: General Formalism and Topological Invariants for 230 Space Groups
• Edge-state enhanced transport in a 2-dimensional quantum walk
• Wannier representation of Floquet topological states
• From Bosonic Topological Transition to Symmetric Fermion Mass Generation
• Metallic Interface Emerging at Magnetic Domain Wall of Antiferromagnetic Insulator---Fate of Extinct Weyl Electrons
• Non-Hermitian Floquet Topological Matter -- A Review
• Conversion rules for Weyl points and nodal lines in topological media
• Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions
• Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism
• Symmetry indicators for topological superconductors
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Finite-size energy gap in weak and strong topological insulators
• Quantum gyro-electric effect: Photon spin-1 quantization in continuum topological bosonic phases
• Topological phase transitions in multi-component superconductors
• Topological Edge Modes by Smart Patterning
• The Bulk-Edge Correspondence for Disordered Chiral Chains
• Time Reversal Symmetric Topological Exciton Condensate in Bilayer HgTe Quantum Wells
• Local and nonlocal order parameters in the Kitaev chain
• Realization of a Z classified chiral-symmetric higher-order topological insulator in a coupling-inversion acoustic crystal
• Exceptional band touching for strongly correlated systems in equilibrium
• Quasi 1D topological nodal vortex line phase in doped superconducting 3D Dirac Semimetals
• Correlated spinless fermions on the honeycomb lattice revisited
• Exotic topological density waves in cold atomic Rydberg fermions
• Electric Field Tunable Topological Phases in Graphene Nanoribbons
• Index pairings in presence of symmetries with applications to topological insulators
• Anderson localization and the topology of classifying spaces
• Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
• Probe of Three-Dimensional Chiral Topological Insulators in an Optical Lattice
• Magnetic Field Response and Chiral Symmetry of Time Reversal Invariant Topological Superconductors
• Crossing-Line-Node Semimetals: General Theory and Application to Rare-Earth Trihydrides
• Andreev reflection from a topological superconductor with chiral symmetry
• Towards a mathematical formalism for classifying phases of matter
• Topological classification of adiabatic processes
• Creating anomalous Floquet Chern insulators with magnetic quantum walks
• Electric circuit simulations of $n$th-Chern insulators in $2n$-dimensional space and their non-Hermitian generalizations for arbitral $n$
• Phonon-induced Floquet second-order topological phases protected by space-time symmetries
• Majorana corner modes with solitons in an attractive Hubbard-Hofstadter model of cold atom optical lattices
• Classification of "Real" Bloch-bundles: Topological quantum systems of type AI
• Topological superconductivity in planar Josephson junctions: Narrowing down to the nanowire limit
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• Hermitian Bulk -- Non-Hermitian Boundary Correspondence
• Topological Invariant and Anomalous Edge Modes of Strongly Nonlinear Systems
• Bulk-edge correspondence of classical diffusion phenomena
• Fragile topological phases in interacting systems
• Higher Dimensional Quantum Hall Effect as A-Class Topological Insulator
• The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors
• Free-Fermionic Topological Quantum Sensors
• Minimal non-abelian nodal braiding in ideal metamaterials
• Direct prediction of corner state configurations from edge winding numbers in 2D and 3D chiral-symmetric lattice systems
• Topological Edge States and Fractional Quantum Hall Effect from Umklapp Scattering
• Exact Higher-order Bulk-boundary Correspondence of Corner-localized States
• Emerging Dirac and Majorana fermions for carbon nanotubes with proximity-induced pairing and spiral magnetic field
• A noncommutative framework for topological insulators
• Random-matrix theory of Andreev reflection from a topological superconductor
• Direct Probe of Topological Order for Cold Atoms
• Andreev spectroscopy and surface density of states for a three-dimensional time-reversal invariant topological superconductor
• Topological Edge States with Zero Hall Conductivity in a Dimerized Hofstadter Model
• Topological Properties of Time Reversal Symmetric Kitaev Chain and Applications to Organic Superconductors
• The influence of lattice termination on the edge states of the quantum spin Hall insulator monolayer $1T^{\prime }$-WTe${}_2$
• High-order topological insulators from high-dimensional Chern insulators
• Machine learning topological phases in real space
• Classification of engineered topological superconductors
• 2D and 3D topological insulators with isotropic and parity-breaking Landau levels
• A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
• Topological Route to New and Unusual Coulomb Spin Liquids
• Stabilizing multiple topological fermions on a quantum computer
• CPT theorem and classification of topological insulators and superconductors
• Excess charges as a probe of one-dimensional topological crystalline insulating phases
• Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains
• Effect of photonic spin-orbit coupling on the topological edge modes of a Su-Schrieffer-Heeger chain
• Time reversal invariant topological superconductivity in correlated non-centrosymmetric systems
• Dissipation-induced topological insulators: A no-go theorem and a recipe
• Majorana Excitations, Spin- and Mass Currents on the Surface of Topological Superfluid ${}^3$He-B
• Wire constructions of Abelian topological phases in three or more dimensions
• Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling
• Topological Paramagnetism in Frustrated Spin-One Mott Insulators
• Symmetry Protected Topological Metals
• Gross-Neveu-Wilson model and correlated symmetry-protected topological phases
• Higher winding number in a non-unitary photonic quantum walk
• Critical theories of phase transition between symmetry protected topological states and their relation to the gapless boundary theories
• Topological input-output theory for directional amplification
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Simulation of Higher-Order Topological Phases and Related Topological Phase Transitions in a Superconducting Qubit
• Topological properties of chains of magnetic impurities on a superconducting substrate: Interplay between the Shiba band and ferromagnetic wire limits
• Möbius topological superconductivity in UPt${}_3$
• Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials
• Non-Hermitian Majorana modes protect degenerate steady states
• Universal topological marker
• Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility
• Stroboscopic Symmetry-Protected Topological Phases
• Helical Liquids in Semiconductors
• Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems
• Wigner-Poisson statistics of topological transitions in a Josephson junction
• Transport through a quantum spin Hall quantum dot
• Topological insulators with SU(2) Landau levels
• Topological pi Josephson junction in superconducting Rashba wires
• Three-dimensional Chiral Lattice Fermion in Floquet Systems
• Edge currents as a signature of flat bands in topological superconductors
• Topological space-time crystal
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Tensor Berry connections and their topological invariants
• Antiferromagnetic nuclear spin helix and topological superconductivity in ${}^{13}$C nanotubes
• All-fermion electrodynamics and fermion number anomaly inflow
• Topological Superconductors on Superstring Worldsheets
• From triple-point materials to multiband nodal links
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Bulk and edge-state arcs in non-hermitian coupled-resonator arrays
• Topological Frequency Conversion in a Driven Dissipative Quantum Cavity
• Snake states and their symmetries in graphene
• Topological and symmetry broken phases of Z_N parafermions in one dimension
• Disorder-induced Majorana zero modes in a dimerized Kitaev superconductor chain
• Periodic Table of SYK and supersymmetric SYK
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Superconducting doped topological materials
• Majorana and parafermion corner states from two coupled sheets of bilayer graphene
• Mott-Superfluid Transition for Spin-Orbit Coupled Bosons in One-Dimensional Optical Lattices
• Local Topological Markers in Odd Spatial Dimensions and Their Application to Amorphous Topological Matter
• Majorana modes in emergent-wire phases of helical and cycloidal magnet-superconductor hybrids
• Chern mosaic - topology of chiral superconductivity on ferromagnetic adatom lattices
• Homotopy Theory of Strong and Weak Topological Insulators
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Conductivity of a Weyl semimetal with donor and acceptor impurities
• On the Bott index of unitary matrices on a finite torus
• $Z_N$ Berry Phases in Symmetry Protected Topological Phases
• Robustness of topological corner modes against disorder and application to acoustic networks
• Unusual magnetic phases in the strong interaction limit of two-dimensional topological band insulators in transition metal oxides
• Circuit realisation of a two-orbital non-Hermitian tight-binding chain
• Criticality of the metal-topological insulator transition driven by disorder
• Superconductivity without inversion and time-reversal symmetries
• Fractional charge bound to a vortex in two dimensional topological crystalline insulators
• Majorana flat bands, chiral Majorana edge states, and unidirectional Majorana edge states in noncentrosymmetric superconductors
• Three-dimensional topological magnon systems
• Non-local topological electromagnetic phases of matter
• Higher-order topological superconductors based on weak topological insulators
• Bulk-Defect Correspondence in Particle-Hole Symmetric Insulators and Semimetals
• Topological septet pairing with spin-$\frac{3}{2}$ fermions -- high partial-wave channel counterpart of the ${}^3$He-B phase
• An operator-based approach to topological photonics
• Perspective: Strongly correlated and topological states in [111] grown transition metal oxide thin films and heterostructures
• Tuning topological superconductivity in helical Shiba chains by supercurrent
• $(k,n)$-fractonic Maxwell theory
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Inter-orbital topological superconductivity in spin-orbit coupled superconductors with inversion symmetry breaking
• ${\mathbb{Z}}_2$ invariants of topological insulators as geometric obstructions
• Topological invariant for generic 1D time reversal symmetric superconductors in class DIII
• A gauge theory generalization of the fermion-doubling theorem
• Fracton physics of spatially extended excitations
• Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals
• Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
• Non-Hermitian topology in monitored quantum circuits
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Exhaustive List of Topological Hourglass Band Crossings in 230 Space Groups
• Realizing topological surface states in a lower-dimensional flat band
• The Topological Relation Between Bulk Gap Nodes and Surface Bound States : Application to Iron-based Superconductors
• Topological and non-topological features of generalized Su-Schrieffer-Heeger models
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• The interacting Rice-Mele model: bulk and boundaries
• Controlled Creation of Quantum Skyrmions
• Low-field Topological Threshold in Majorana Double Nanowires
• Models of three-dimensional fractional topological insulators
• Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
• Topological superconductivity induced by a triple-Q magnetic structure
• Paramagnetically induced gapful topological superconductors
• Topological Classification Table Implemented with Classical Passive Meta-Materials
• Persistent currents in Dirac fermion rings
• Corner states of topological fullerenes
• Designing flat-band tight-binding models with tunable multifold band touching points
• Large-scale GHZ states through topologically protected zero-energy mode in a superconducting qutrit-resonator chain
• Optical manifestations and bounds of topological Euler class
• Odd-Frequency Pairs in Chiral Symmetric Systems: Spectral Bulk-Boundary Correspondence and Topological Criticality
• Quantum Field Theory Anomalies in Condensed Matter Physics
• Induced spin texture in semiconductor/topological insulator heterostructures
• Anisotropic topological superconductivity in Josephson junctions
• Anomalous Nernst effect in type-II Weyl semimetals
• Topological characterization of classical waves: the topological origin of magnetostatic surface spin waves
• Quantized topological energy pumping and Weyl points in Floquet synthetic dimensions with a driven-dissipative photonic molecule
• Topological order of mixed states in quantum many-body systems
• Fidelity susceptibility near topological phase transitions in quantum walks
• Square-root topological phase with time-reversal and particle-hole symmetry
• Majorana surface modes of nodal topological pairings in spin-$\frac{3}{2}$ semi-metals
• Squaring the fermion: The threefold way and the fate of zero modes
• Chiral topological phases and fractional domain wall excitations in one-dimensional chains and wires
• Surface electronic state of superconducting topological crystalline insulator
• Phase structure of the interacting Su-Schrieffer-Heeger model and the relationship with the Gross-Neveu model on lattice
• Angular momentum and topology in semiconducting single-wall carbon nanotubes
• Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1D
• Hyperbolic non-Abelian semimetal
• Local markers for crystalline topology
• Robustness of symmetry-protected topological states against time-periodic perturbations
• Topological states in arrays of optical waveguides engineered via mode interference
• Topological Superconductivity in an s-wave Superconductor and Its Implication to Iron-based Superconductors
• Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice
• Topological Insulators and Quantum Spin Liquids
• Sublattice dynamics and quantum state transfer of doublons in two-dimensional lattices
• Topological invariants for interacting topological insulators: II. Breakdown of the Green's function formalism
• Universal platform of point-gap topological phases from topological materials
• Symmetry-enforced many-body separability transitions
• Quantum topology identification with deep neural networks and quantum walks
• Probing topological superconductors with emergent gravity
• Synthetic Weyl Points and Chiral Anomaly in Majorana Devices with Nonstandard Andreev-Bound-State Spectra
• Read-Green resonances in a topological superconductor coupled to a bath
• Robust topological order in fermionic ${\mathbb{Z}}_2$ gauge theories: from Aharonov-Bohm instability to soliton-induced deconfinement
• Symmetry indicator in non-Hermitian systems
• Classical Spin Spirals in Frustrated Magnets from Free-Fermion Band Topology
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Quantum many-body topology of quasicrystals
• Ring Dirac Solitons in Nonlinear Topological Lattices
• Delocalization Transition of Disordered Axion Insulator
• Trapped state at a dislocation in a weak magnetomechanical topological insulator
• Topological dynamics and excitations in lasers and condensates with saturable gain or loss
• Classifying topology in photonic heterostructures with gapless environments
• Weyl Semimetal and Topological Phase Transition in Five Dimensions
• Topology and entanglement in quench dynamics
• Antiferromagnetic topological insulator state in the correlated Bernevig-Hughes-Zhang model
• Unraveling the topology of dissipative quantum systems
• Symmetry-protected topological states for interacting fermions in alkaline-earth-like atoms
• Chern-Simons Theory and Wilson Loops in the Brillouin Zone
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Robustness of Majorana bound states in the short junction limit
• Bulk detection of time-dependent topological transitions in quenched chiral models
• D-Algebra Structure of Topological Insulators
• Topological superconductivity from magnetic impurities on monolayer NbSe${}_2$
• Edge States: Topological Insulators, Superconductors and QCD Chiral Bags
• Quadratic pseudospectrum for identifying localized states
• The classification of surface states of topological insulators and superconductors with magnetic point group symmetry
• Topological Insulators and Superconductors from String Theory
• Quantum Monte Carlo study of strange correlator in interacting topological insulators
• Amorphous topological phases protected by continuous rotation symmetry
• Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems
• 3D Dirac Electrons on a Cubic Lattice with Noncoplanar Multiple-Q Order
• Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence
• Phase-dependent Andreev molecules and superconducting gap closing in coherently coupled Josephson junctions
• X-shaped and Y-shaped Andreev resonance profiles in a superconducting quantum dot
• Topological states and quantized current in helical molecules
• Thermodynamic signatures of edge states in topological insulators
• Resonant Raman scattering theory for Kitaev models and their Majorana fermion boundary modes
• Unconventional pairing and electronic dimerization instabilities in the doped Kitaev-Heisenberg model
• Spin-directed network model for the surface states of weak three-dimensional ${\mathbb{Z}}_2^{}$ topological insulators
• Flat-band-based multifractality in the all-band-flat diamond chain
• Josephson effect in superconducting wires supporting multiple Majorana edge states
• Space, matter and topology
• Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model
• Construction of real-valued localized composite Wannier functions for insulators
• Superfluid 3He in a restricted geometry with a perpendicular magnetic field
• Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
• Topological characterization and stability of Floquet Majorana modes in Rashba nanowire
• Revealing Topology in Metals using Experimental Protocols Inspired by $K$-Theory
• Stability of surface states of weak ${\mathbb{Z}}_2$ topological insulators and superconductors
• Determining topological order from a local ground state correlation function
• Competing Vortex Topologies in Iron-based Superconductors
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Three Dimensional Z2 Topological Phases enriched by Time-Reversal Symmetry
• Flux-fusion anomaly test and bosonic topological crystalline insulators
• Nonanalyticity of circuit complexity across topological phase transitions
• Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces
• $N$-band Hopf insulator
• Full proximity treatment of topological superconductors in Josephson-junction architectures
• Realization of an atomic quantum Hall system in four dimensions
• Multiband s-wave topological superconductors: role of dimensionality and magnetic field response
• Metallic phase of the quantum Hall effect in four-dimensional space
• Realizing and detecting a topological insulator in the AIII symmetry class
• Unidirectional Maxwellian Spin Waves
• Wannier functions and Z_2 invariants in time-reversal symmetric topological insulators
• Topology of multipartite non-Hermitian one-dimensional systems
• Topological superconductivity in ferromagnetic atom chains beyond the deep-impurity regime
• Tunneling spectroscopy of topological superconductors
• Complete homotopy invariants for translation invariant symmetric quantum walks on a chain
• Symmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Topologically nontrivial Andreev bound states
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• Classification of Mixed State Topology in One Dimension
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice
• Topological number and Fermion Green's function of Strongly Interacting Topological Superconductors
• Floquet engineering of individual band gaps in an optical lattice using a two-tone drive
• Random-matrix theory of thermal conduction in superconducting quantum dots
• Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies
• Topological Insulators and Superconductors from D-branes
• Disordered Weyl semimetals and their topological family
• Symmetry-resolved entanglement entropy in critical free-fermion chains
• Anisotropic magnetic responses of topological crystalline superconductors
• Electromagnetic and thermal responses of Z topological insulators and superconductors in odd spatial dimensions
• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors
• Chiral Topological Insulator on Nambu 3-Algebraic Geometry
• Euler Obstructed Cooper Pairing: Nodal Superconductivity and Hinge Majorana Zero Modes
• Chiral topological insulator of magnons
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Topological and conventional phases of a three dimensional electron glass
• Symmetry-based approach to nodal structures: Unification of compatibility relations and gapless point classifications
• Antiferromagnetic topological insulators in cold atomic gases
• Quench dynamics of fermion-parity switches in a Josephson junction
• Finite-temperature topological invariant for interacting systems
• Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder
• Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• Correlation effects on topological crystalline insulators
• Thermal metal-insulator transition in a helical topological superconductor
• Magnetic impurities at quantum critical points: large-$N$ expansion and SPT connections
• Quantum criticality at the Chern-to-normal insulator transition
• Nodal Andreev Spectra in Multi-Majorana Three-Terminal Josephson Junctions
• Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way
• Fate of Majorana modes in ${\mathrm{CeCoIn}}_5$/${\mathrm{YbCoIn}}_5$ superlattices -a test bed for reduction of topological classification-
• Counting Majorana zero modes in superconductors
• Realization of a one-dimensional topological insulator in ultrathin germanene nanoribbons
• Interaction Enabled Topological Crystalline Phases
• The New Phase due to Symmetry Protected Piecewise Berry Phases; Enhanced Pumping and Non-reciprocity in Trimer Lattices
• Disorder Protected and Induced Local Zero-Modes in Longer-Range Kitaev Chains
• Bridging the gap between topological non-Hermitian physics and open quantum systems
• Seeing bulk topological properties of band insulators in small photonic lattices
• Systematic Construction of tight-binding Hamiltonians for Topological Insulators and Superconductors
• Probing the topological properties of the Jackiw-Rebbi model with light
• Dissipative analog of four-dimensional quantum Hall physics
• Stability of flat-band edge states in topological superconductors without inversion center
• Influence of the impurity scattering on charge transport in unconventional superconductor junctions
• Central Charge of Periodically Driven Critical Kitaev Chains
• Magnetic-Field-Induced Topological Reorganization of a P-wave Superconductor
• Dimensional hierarchy of fermionic interacting topological phases
• Majorana bound states in hybrid 2D Josephson junctions with ferromagnetic insulators
• The anisotropic Harper-Hofstadter-Mott model: competition between condensation and magnetic fields
• Study of the phase diagram of the Kitaev-Hubbard chain
• Bulk-edge correspondence for nonlinear eigenvalue problems
• Topological invariants to characterize universality of boundary charge in one-dimensionalinsulators beyond symmetry constraints
• Weyl-Majorana solenoid
• Uhlmann number in translational invariant systems
• Nontrivial topological states on a Möbius band
• Holographic correspondence in topological superconductors
• Topological polarons, quasiparticle invariants and their detection in 1D symmetry-protected phases
• Locating topological phase transitions using nonequilibrium signatures in local bulk observables
• One-dimensional topological metal
• Topological Floquet edge states in periodically curved waveguides
• Local Noether theorem for quantum lattice systems and topological invariants of gapped states
• Unification of topological invariants in Dirac models
• Disorder-driven transition in a chain with power-law hopping
• Majorana Bound States in Double Nanowires with Reduced Zeeman Thresholds due to Supercurrents
• Scrambling and decoding the charged quantum information
• Renormalization group flows for Wilson-Hubbard matter and the topological Hamiltonian
• Absence of equilibrium edge currents in theoretical models of topological insulators
• Spin Berry phase in the Fermi arc states
• Holographic fractional topological insulators in 2+1 and 1+1 dimensions
• Topologically protected strongly-correlated states of photons
• Correlated triple-Weyl semimetals with Coulomb interactions
• Topological invariants for the Haldane phase of interacting SSH chains -- a functional RG approach
• Interacting topological quantum chemistry of Mott atomic limits
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Chiral 1D Floquet topological insulators beyond rotating wave approximation
• Finite volume calculation of $K$-theory invariants
• Current fluctuations in unconventional superconductor junctions with impurity scattering
• Effect of Strong Disorder on 3-Dimensional Chiral Topological Insulators: Phase Diagrams, Maps of the Bulk Invariant and Existence of Topological Extended Bulk States
• Topological elasticity of non-orientable ribbons
• Edge insulating topological phases in a two-dimensional long-range superconductor
• Robustness of the helical edge states in topological insulators
• Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries
• Disordered Chern insulator with a two step Floquet drive
• Gauge freedom in observables and Landsbergs nonadiabatic geometric phase: pumping spectroscopy of interacting open quantum systems
• Topological Vortex Phase Transitions in Iron-Based Superconductors
• Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions
• Topological Pair-Density-Wave Superconducting States
• Disorder driven phase transitions in weak AIII topological insulators
• Four-dimensional topological lattices through connectivity
• Interface currents in topological superconductor-ferromagnet heterostructures
• Few-mode geometric description of a driven-dissipative phase transition in an open quantum system
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• The K-Theoretic Bulk-Boundary Principle for Dynamically Patterned Resonators
• Chiral zero modes in superconducting nanowires with Dresselhaus spin-orbit coupling
• Geometric Phases for Mixed States of the Kitaev Chain
• Embedded Topological Insulators
• Majorana zero modes and long range edge correlation in interacting Kitaev chains: analytic solutions and density-matrix-renormalization-group study
• Vacancy-Engineered Flat-Band Superconductivity in Holey Graphene
• Supercurrent-induced topological phase transitions
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• A microwave realization of the chiral orthogonal, unitary, and symplectic ensembles
• Symmetry and Gap Classification of the non-symmorphic SrPtAs
• Universal Finite-Size Scaling around Topological Quantum Phase Transitions
• Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry
• Robustness of topological order against disorder
• A diagnosis scheme for topological degeneracies at high-symmetry momenta
• A classification of magnetic frustration and metamaterials from topology
• Elementary band representations for the single-particle Green's function of interacting topological insulators
• Topological marker approach to an interacting Su-Schrieffer-Heeger model
• Breaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides
• Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors
• Estimating bulk and edge topological indices in finite open chiral chains
• Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• Matrix product states for Hartree-Fock-Bogoliubov wave functions
• Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors
• Entanglement modes and topological phase transitions in superconductors
• Traversable wormhole in coupled SYK models with imbalanced interactions
• T-Duality of Topological Insulators
• Floquet quadrupole photonic crystals protected by space-time symmetry
• Topological braiding of non-Abelian mid-gap defects in classical meta-materials
• Entanglement Spectrum as a Probe for the Topology of a Spin-Orbit Coupled Superconductor
• Spin-orbit Coupling in Optical lattices
• Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators
• Geometric Josephson effects in chiral topological nanowires
• Non-Hermitian Topology in Hermitian Topological Matter
• Robustness of the pumping charge to dynamic disorder
• Chiral Majorana fermions in graphene from proximity-induced superconductivity
• Geometry and Topology Tango in Ordered and Amorphous Chiral Matter
• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
• Fate of exceptional points under interactions: Reduction of topological classifications
• Progress in superconductor-semiconductor topological Josephson junctions
• Observation of a topological edge state stabilized by dissipation
• Surface charge theorem and topological constraints for edge states: An analytical study of one-dimensional nearest-neighbor tight-binding models
• Origin and localization of topological band gaps in gyroscopic metamaterials
• Higher (Odd) Dimensional Quantum Hall Effect and Extended Dimensional Hierarchy
• Topological state engineering by potential impurities on chiral superconductors
• Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices
• Topological pumping in class-D superconducting wires
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Optical $N$-invariant of graphene's viscous Hall fluid
• Topology-dependent quantum dynamics and entanglement-dependent topological pumping in superconducting qubit chains
• Generalized Bloch band theory for non-Hermitian bulk-boundary correspondence
• Magnetoelectrically-Tunable Andreev-Bound-State Spectra and Spin Polarization in P-Wave Josephson Junctions
• One-dimensional topological insulator: a model for studying finite-size effects in topological insulator thin films
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Exotic Topological Types of Majorana Zero-modes and Their Universal Quantum Manipulation
• Probing topology in nonlinear topological materials using numerical $K$-theory
• Dirac surface states in magnonic analogs of topological crystalline insulators
• Link between the photonic and electronic topological phases in artificial graphene
• Novel ${\mathbb{Z}}_2$-topological metals and semimetals
• Dimensional crossover of transport characteristics in topological insulator nanofilms
• Topological boundary invariants for Floquet systems and quantum walks
• Topology detection in cavity QED
• Surface transport coefficients for three-dimensional topological superconductors
• K-Theory for Real C*-algebras via Unitary Elements with Symmetries
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Further insights into the thermodynamics of the Kitaev honeycomb model
• Universal topological quench dynamics: Altland-Zirnbauer tenfold classes
• Electromagnetic and thermal responses in topological matter: topological terms, quantum anomalies and D-branes
• Generalized lattice Wilson-Dirac fermions in (1+1) dimensions for atomic quantum simulation and topological phases
• Topological D+p-wave superconductivity in Rashba systems
• Compactly Supported Wannier Functions and Strictly Local Projectors
• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals
• Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis
• Majorana bound states in a superconducting Rashba nanowire in the presence of antiferromagnetic order
• Disorder and interaction in chiral chains: Majoranas vs complex fermions
• Characterization of edge states in perturbed honeycomb structures
• Chern number and Berry curvature for Gaussian mixed states of fermions
• Theory of tunneling spectroscopy for chiral topological superconductors
• Entanglement properties of the time periodic Kitaev Chain
• Identifying, and constructing, complex magnon band topology
• Luttinger liquid in contact with a Kramers pair of Majorana bound states
• Boundary central charge from bulk odd viscosity - chiral superfluids
• Bulk-boundary correspondence in extended trimer Su-Schrieffer-Heeger model
• Topological invariants for phase transition points of one-dimensional ${\mathbb{Z}}_2$ topological systems
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Reduction of topological $\mathbb{Z}$ classification in cold atomic systems
• Subgap states in two dimensional spectroscopy of unconventional superconductors using graphene
• Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
• Bulk-boundary correspondence and singularity-filling in long-range free-fermion chains
• Paradoxical extension of the edge states across the topological phase transition due to emergent approximate chiral symmetry in a quantum anomalous Hall system
• Effects of non-equilibrium noise on a quantum memory encoded in Majorana zero modes
• Generalized Connes-Chern characters in KK-theory with an application to weak invariants of topological insulators
• Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard
• Modulated Helical Metals at Magnetic Domain Walls of Pyrochlore Iridium Oxides
• A New Numerical Method for ${\mathbb{Z}}_2$ Topological Insulators with Strong Disorder
• Majorana zero modes in gate-defined germanium hole nanowires
• Interacting Symmetry-Protected Topological Phases Out of Equilibrium
• Classification of crystalline topological semimetals with an application to Na${}_3$Bi
• Quantum Control in Open and Periodically Driven Systems
• Topological transport of mobile impurities
• Topological Superfluid and Majorana Zero Modes in Synthetic Dimension
• Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter
• Equality of bulk wave functions and edge correlations in topological superconductors: A spacetime derivation
• Double Majorana vortex zero modes in superconducting topological crystalline insulators with surface rotation anomaly
• Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way
• Strain induced topological phase transition at zigzag edges of monolayer transition-metal dichalcogenides
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Time-reversal symmetric topological metal
• Emerging topological bound states in Haldane model zigzag nanoribbons
• Signatures of dephasing by mirror-symmetry breaking in weak-antilocalization magnetoresistance across the topological transition in Pb${}_{1-x}$Sn${}_x$Se
• Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence
• Quantum Hall transitions: An exact theory based on conformal restriction
• Engineered Open Systems and Quantum Simulations with Atoms and Ions
• Efficient method to compute ${\mathbb{Z}}_4$-indices with glide symmetry and applications to Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$
• Majorana fermion fingerprints in spin-polarised scanning tunneling microscopy
• Unified Topological Response Theory for Gapped and Gapless Free Fermions
• Helical spin texture of surface states in topological superconductors
• Engineering anomalous Floquet Majorana modes and their time evolution in helical Shiba chain
• Topological Aspect of Graphene Patchwork with Regular Arrays of Nano Holes
• Three-fold way of entanglement dynamics in monitored quantum circuits
• Non-Local Annihilation of Weyl Fermions in Correlated Systems
• Parity-doublet representation of Majorana fermions and neutron oscillation
• Density of states at disorder-induced phase transitions in a multichannel Majorana wire
• Theory of oblique topological insulators
• Multiplicative topological phases
• Duality of Topological Edge States in a Mechanical Kitaev Chain
• A proposed signature of Anderson localization and correlation-induced delocalization in an N-leg optical lattice
• Topological Kondo insulators in one dimension: Continuous Haldane-type ground-state evolution from the strongly-interacting to the non-interacting limit
• Robustness of chiral edge modes in fractal-like-lattices below two dimensions: A case study
• Arbitrary synthetic dimensions via multi-boson dynamics on a one-dimensional lattice
• Strain topological metamaterials
• A supervised learning algorithm for interacting topological insulators based on local curvature
• Bosonic symmetry protected topological phases with reflection symmetry
• Effect of chiral symmetry on chaotic scattering from Majorana zero modes
• Interference of Majorana fermions in NS junctions
• Topological properties of a generalized spin-orbit-coupled Su-Schrieffer-Heeger model
• Topological Polaritons in a Quantum Spin Hall Cavity
• Magnetic end-states in a strongly-interacting one-dimensional topological Kondo insulator
• Effects of Defects and Dephasing on Charge and Spin Currents in Two-Dimensional Topological Insulators
• Exceptional point description of one-dimensional chiral topological superconductors/superfluids in BDI class
• Quantum distance and the Euler number index of the Bloch band in a 1D spin model
• Topological insulators and topological non-linear sigma models
• Majorana nanowires, Kitaev chains, and spin models
• Rashba Sandwiches with Topological Superconducting Phases
• Variants of the symmetry-based indicator
• Topological Edge and Interface states at Bulk disorder-to-order Quantum Critical Points
• Analytic approach to quantum metric and optical conductivity in Dirac models with parabolic mass in arbitrary dimensions
• Topology of critical chiral phases: multiband insulators and superconductors
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Tight-binding billiards
• Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly
• Topological insulators and superconductors based on $p$-wave magnets,electrical control and detection of a domain wall
• New types of topological superconductors under local magnetic symmetries
• Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains
• Composite Spin Liquid in Correlated Topological Insulator - Spin Liquid without Spin-Charge Separation
• Topological Solitons in Su-Schrieffer-Heeger Chain with periodic hopping modulation, domain walls and disorder
• Topological characterization of one-dimensional open fermionic systems
• Higher Berry Phase of Fermions and Index Theorem
• Origin of Topological Surface Superconductivity in FeSe${}_{0.45}$Te${}_{0.55}$
• Finite-temperature effective boundary theory of the quantized thermal Hall effect
• Global phase diagram of two-dimensional Dirac fermions in random potentials
• Topological protection of Majorana polaritons in a cavity
• Stabilization of Hubbard-Thouless pumps through nonlocal fermionic repulsion
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors
• Search for localized Wannier functions of topological band structures via compressed sensing
• Phase-locked magnetoconductance oscillations as a probe of Majorana edge states
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Localization persisting under aperiodic driving
• Topological phases: isomorphism, homotopy and $K$-theory
• Kramers' degeneracy for open systems in thermal equilibrium
• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Haldane phase in one-dimensional topological Kondo insulators
• Sputtering induced re-emergence of the topological surface state in Bi${}_2$Se${}_3$
• Phase diagram of two interacting helical states
• Topological Number of Edge States
• Effective response theory for Floquet topological systems
• Dimerization-induced topological superconductivity in a Rashba nanowire
• Quantum walks: Schur functions meet symmetry protected topological phases
• Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors
• Catalogue of Andreev spectra and Josephson effects in structures with time-reversal-invariant topological superconductor wires
• Novel topological insulators from crystalline symmetries
• Catalog of noninteracting tight-binding models with two energy bands in one dimension
• Field theory of non-Hermitian disordered systems
• Interaction Protected Topological Insulators with Time Reversal Symmetry
• Surface field theories of point group symmetry protected topological phases
• Bulk-boundary correspondance for Sturmian Kohmoto like models
• Spinon pairing induced by chiral in-plane exchange and the stabilization of odd-spin Chern number spin liquid in twisted ${\mathrm{MoTe}}_2$
• Topological states in disordered arrays of dielectric nanoparticles
• Real Hopf Insulator
• Topological states in normal and superconducting $p$-wave chains
• Finite-size Topology
• An infinite family of 3d Floquet topological paramagnets
• Geometric Model of Topological Insulators from the Maxwell Algebra
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Colloquium: Synthetic quantum matter in non-standard geometries
• Thermal conductance as a probe of the non-local order parameter for a topological superconductor with gauge fluctuations
• Monopole Charge Density Wave States in Weyl Semimetals
• Uncovering Weyl Fermions in the Quantum Limit of NbP
• Majorana multipole response: General theory and application to wallpaper groups
• Three-Dimensional Fractional Topological Insulators in Coupled Rashba Layers
• Beyond the constant-mass Dirac physics: Solitons, charge fractionization, and the emergence of topological insulators in graphene rings
• Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor
• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids
• Dynamical Phase Transitions in Topological Insulators
• Floquet second-order topological Anderson insulator hosting corner localized modes
• Embedded Topological Semimetals
• Hinge Magnons from Non-collinear Magnetic Order in Honeycomb Antiferromagnet
• Bosonic Short Range Entangled states Beyond Group Cohomology classification
• Superconductivity in two-dimensional disordered Dirac semimetals
• Helical Majorana surface states of strongly disordered topological superconductors with time-reversal symmetry
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Topological linear response of hyperbolic Chern insulators
• Three-Band Model for Quantum Hall and Spin Hall Effects
• Topological Superfluids and BEC-BCS Crossover in Attractive Haldane-Hubbard Model
• Fragility of surface states in non-Wigner Dyson topological insulators
• Dynamical competition between Quantum Hall and Quantum Spin Hall effects
• Topological gauge theory for mixed Dirac stationary states in all dimensions
• Majorana edge magnetization in the Kitaev honeycomb model
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Quench dynamics and bulk-edge correspondence in nonlinear mechanical systems
• Higher order topological matter and fractional chiral states
• Revealing the boundary Weyl physics of the four-dimensional Hall effect via phason engineering in metamaterials
• Driven-dissipative topological phases in parametric resonator arrays
• Quantum geometry of singlet superconductors
• Anomalous electromagnetic response of superconducting Rashba systems in trivial and topological phases
• Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$
• Effective field theories of topological crystalline insulators and topological crystals
• Topology in time-reversal symmetric crystals
• Magnetic Flux Periodicity in Second Order Topological Superconductors
• Spin Conductance and Spin Conductivity in Topological Insulators: Analysis of Kubo-like terms
• On the topological character of three-dimensional Nexus triple point degeneracies
• Phase-dependent heat transport in Josephson junctions with p-wave superconductors and superfluids
• Equivalence of Topological Insulators and Superconductors
• Scattering theory of topological invariants in nodal superconductors
• Topological Quantum Walk with Discrete Time-Glide Symmetry
• Topological Modes in One Dimensional Solids and Photonic Crystals
• Anomalous localization at the boundary of an interacting topological insulator
• Magnetic Response of Majorana Kramers Pairs Protected by Z2 Invariants
• Quantum phase transition of fracton topological orders
• Time-reversal-breaking topological phases in antiferromagnetic Sr${}_2$FeOsO${}_6$ films
• Rational boundary charge in one-dimensional systems with interaction and disorder
• Band spectrum is D-brane
• Structure of vortex-bound states in spin-singlet chiral superconductors
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Topological Dipole Conserving Insulators and Multipolar Responses
• Dielectric and optical markers originating from quantum geometry
• A simple approach to characterizing band topology in bosonic pairing Hamiltonians
• Non-Abelian Half-Quantum Vortices in ${}^3{P}_2$ Topological Superfluids
• Fractional hinge and corner charges in various crystal shapes with cubic symmetry
• Topological classification of intrinsic 3D superconductors using anomalous surface construction
• Stability of entanglement-spectrum crossing in quench dynamics of one dimensional gapped free-fermion systems
• Finite temperature geometric properties of the Kitaev honeycomb model
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• Hidden zero modes and topology of multiband non-Hermitian systems
• Optical absorption measurement of spin Berry curvature and spin Chern marker
• One-dimensional non-interacting topological insulators with chiral symmetry
• Cataloging topological phases of $N$-stacked Su-Schrieffer-Heeger chains by a systematic breaking of symmetries
• Symmetric non-Hermitian skin effect with emergent nonlocal correspondence
• Haldane model on the Sierpiński gasket
• Magnetic manipulation of topological states in p-wave superconductors
• Topological flat bands in optical checkerboard-like lattices
• Topological Floquet states on a Möbius band irradiated by circularly polarised light
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Anomalous Kerr Effect in SrRuO${}_3$ Thin Films
• String and conventional order parameters in the solvable modulated quantum chain
• On topological transitions in metals
• Gapless edge states and their stability in two-dimensional quantum magnets
• Three-dimensional Topological Insulators and Bosonization
• Disorder lines, modulation, and partition function zeros in free fermion models
• Theory of local ${\mathbb{Z}}_2$ topological markers for finite and periodic two-dimensional systems
• Polar phase of superfluid ${}^3$He: Dirac lines in the parameter and momentum spaces
• Doubling Theorem and Boundary States of Five-Dimensional Weyl Semimetal
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue
• Topologically distinct atomic insulators
• The KO-valued spectral flow for skew-adjoint Fredholm operators
• Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum
• Time-reversal Invariant SU(2) Hofstadter Problem in Three Dimensional Lattices
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Bulk-edge correspondence with generalized chiral symmetry
• Engineering of Chern insulators and circuits of topological edge states
• Nonlinear Hall effect in two-dimensional class AI metals
• Interplay between altermagnetism and topological superconductivity on an unconventional superconducting platform
• Topological $Z_2$ invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group
• Weyl Semimetallic State in the Rashba-Hubbard Model
• Stability of Disordered Topological Superconducting Phases in Magnet--Superconductor Hybrid Systems
• Toward simulation of topological phenomenas with one-, two- and three-dimensional quantum walks
• Zeros of Green Functions in Topological Insulators
• Haldane Model at finite temperature
• Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena
• Inherited topological superconductivity in two-dimensional Dirac semimetals
• Thermodynamic and spectral properties of adiabatic Peierls chains
• Phase diagram of a model for topological superconducting wires
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Gauging anomalous unitary operators
• Uniaxial Strain Induced Topological Phase Transition in Bismuth-Tellurohalide-Graphene Heterostructures
• Fractional Electromagnetic Response in Three-Dimensional Chiral Anomalous Semimetal
• $\pi$-fluxes, semi-metals and flat bands in artificial materials
• Subradiant edge states in an atom chain with waveguide-mediated hopping
• Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
• Time-reversal-invariant topological superconductivity
• Su-Schrieffer-Heeger quasicrystal: Topology, localization, and mobility edge
• Network model for higher-order topological phases
• Topological thermoelectric effects in spin-orbit coupled electron and hole doped semiconductors
• Trapping Majorana Zero Modes in Vortices of Magnetic Texture Crystals Coupled to Nodal Superconductors
• Interacting Topological Insulators with Synthetic Dimensions
• Flat Energy Bands within Antiphase and Twin Boundaries and at Open Edges in Topological Materials
• Quantum skyrmion Hall effect
• Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines
• Computing classification of interacting fermionic symmetry-protected topological phases using topological invariants
• Universal Higher-Order Topology from 5D Weyl semimetal: Edge topology, edge Hamiltonian and nested Wilson loop
• Non-local order parameters for states with topological electromagnetic response
• Translation symmetry-enriched toric code insulator
• Non-abelian bosonization in two and three spatial dimensions and applications
• Floating Edge Bands in the Bernevig-Hughes-Zhang model with Altermagnetism
• Characterization of topological insulators based on the electronic polarization with spiral boundary conditions
• Chirality-induced emergent spin-orbit coupling in topological atomic lattices
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• First principles study of topological phase in chains of $3d$ transition metals
• Scaling behavior in a multicritical one-dimensional topological insulator
• Floquet simulators for topological surface states in isolation
• Bosonic Topological Excitations from the Instability of a Quadratic Band Crossing
• Electron Correlation Effects on Topological Phases
• Quench dynamics of Hopf insulators
• Asymptotically exact photonic analogues of chiral symmetric topological tight-binding models
• Anatomy of Z2 fluxes in anyon Fermi liquids and Bose condensates
• Quantum geometrical properties of topological materials
• Topological effective field theories for Dirac fermions from index theorem
• Symmetry-Resolved Entanglement: General considerations, calculation from correlation functions, and bounds for symmetry-protected topological phases
• Symmetry-Protected Topological Phase for Spin-Tensor-Momentum-Coupled Ultracold Atoms
• On the relation of the entanglement spectrum to the bulk polarization
• Topologically Protected Edge States in Triangular Lattices
• Interacting Valley Chern Insulator and its Topological Imprint on Moiré Superconductors
• Topological BF theory of the quantum hydrodynamics of incompressible polar fluids
• Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory
• Inequivalent $Z_2^n$-graded brackets, $n$-bit parastatistics and statistical transmutations of supersymmetric quantum mechanics
• Stability of zero energy Dirac touchings in the honeycomb Hofstadter problem
• Topological Mott transition in a Weyl-Hubbard model with dynamical mean-field theory
• Topological circuit of a versatile non-Hermitian quantum system
• Self-localized topological states in three dimensions
• Discrete symmetries of low-dimensional Dirac models: A selective review with a focus on condensed-matter realisations
• Simulating Floquet topological phases in static systems
• Absence of topology in Gaussian mixed states of bosons
• Topological skyrmion phases of matter
• Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
• Hilbert space inner products for PT-symmetric Su-Schrieffer-Heeger models
• Topological phases of parafermionic chains with symmetries
• Hidden Symmetry Decoupling of Majorana Fermions
• Generating and detecting topological phases with higher Chern number
• Majorana fermions in topological insulator nanowires: from single superconducting nanowires to Josephson junctions
• Topological Phases emerging from Spin-Orbital Physics
• Nodal pair density waves from a quarter-metal in crystalline graphene multilayers
• Statistics tuned entanglement of the boundary modes in coupled Su-Schrieffer-Heeger chains
• Detecting the spread of valence band Wannier functions by optical sum rules
• Generalized Thouless Pumps in 1+1-dimensional Interacting Fermionic Systems
• Strain manipulation of Majorana fermions in graphene armchair nanoribbons
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Time-Reversal Invariant Topological Superconductivity in Planar Josephson Bijunction
• Quantum Hall Effect on Odd Spheres
• Hannay Angle: Yet Another Symmetry Protected Topological Order Parameter in Classical Mechanics
• Disorder effects on thermal transport on the surface of topological superconductors by the self-consistent Born approximation
• Topological properties of a periodically driven Creutz ladder
• Geodesic geometry of 2+1-D Dirac materials subject to artificial, quenched gravitational singularities
• Finite Temperature Entanglement Negativity of Fermionic Symmetry Protected Topological Phases and Quantum Critical Points in One Dimension
• Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
• Multi-Dimensional Quantum Walks: a Playground of Dirac and Schrödinger Particles
• Magnetic Flux Response of Non-Hermitian Topological Phases
• Mechanisms for Magnetic Skyrmion Catalysis and Topological Superconductivity
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Protected Gapless Edge States In Trivial Topology
• Driven one-dimensional noisy Kitaev chain
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Rigorous Index Theory for One-Dimensional Interacting Topological Insulators
• Complex magnetic ground states and topological electronic phases of atomic spin chains on superconductors
• Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems
• Dispersive 1D Majorana modes with emergent supersymmetry in 1D proximitized superconductors via spatially-modulated potentials and magnetic fields
• Flat bands and $Z_2$ topological phases in a non-Abelian kagome lattice
• Topological signatures of the coexistence of antiferromagnetism and odd-parity spin-triplet superconductivity
• Modified Szego-Widom Asymptotics for Block Toeplitz Matrices with Zero Modes
• $SU(3)$ Topological Insulators in the Honeycomb Lattice
• Driving Topological Phases by Spatially Inhomogeneous Pairing Centers
• Core structures of vortices in Ginzburg-Landau theory for neutron ${}^3{P}_2$ superfluids
• Wannier band transitions in disordered $\pi$-flux ladders
• Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields
• Topological superconductivity and anti-Shiba states in disordered chains of magnetic adatoms
• Relativistic non-Fermi liquid from interacting birefringent fermions: A robust superuniversality
• Topological end states due to inhomogeneous strains in wrinkled semiconducting ribbons
• Transport signatures of interacting fermions in quasi-one-dimensional topological superconductors
• Chiral Gravitomagnetic Effect in Topological Superconductors and Superfluids
• Detecting topological transitions in two dimensions by Hamiltonian evolution
• Impurity Effects on Bound States in the Vortex Core of Topological S-wave Superconductor
• Robust zero-energy bound states in a helical lattice
• Wiedemann-Franz-type relation between shot noise and thermal conduction of Majorana surface states in a three-dimensional topological superconductor
• Topological invariants for the fractional quantum Hall states
• Edge states for topological insulators in two dimensions and their Luttinger-like liquids
• Thermodynamics and entanglement entropy of the non-Hermitian SSH model
• Multiple polaritonic edge states in a Su-Schrieffer-Heeger chain strongly coupled to a multimode cavity
• Topological insulators with arbitrarily tunable entanglement
• Anomalous Floquet Phases. A resonance phenomena
• Boundary-induced dynamics in 1D topological systems and memory effects of edge modes
• Exact scaling of geometric phase and fidelity susceptibility and their breakdown across the critical points
• Massless Dirac fermions on a space-time lattice with a topologically protected Dirac cone
• Electromagnetic Response of Three-dimensional Topological Crystalline Insulators
• Ginzburg-Landau description of twin boundaries in noncentrosymmetric superconductors
• Diagnosing Topological Phase Transitions in 1D Superconductors using Berry Singularity Markers
• ${\mathbb{Z}}_2$ topological invariants for mixed states of fermions in time-reversal invariant band structures
• Topologically localized insulators
• Corroborating the bulk-edge correspondence in weakly interacting 1D topological insulators
• Real-space effects of a quench in the Su-Schrieffer-Heeger model and elusive dynamical appearance of the topological edge states
• Unified low-energy effective Hamiltonian and the band topology of $p$-block square-net layer derivatives
• Stability of dynamical topology against dynamical noise in quantum quenches
• Engineering Topological Models with a General-Purpose Symmetry-to-Hamiltonian Approach
• Quantized transport induced by topology transfer between coupled one-dimensional lattice systems
• Interplay between short and long-range entanglement in symmetry protected phases
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Finite-size topological phases from semimetals
• Many-Body Chern Numbers of $\nu =1/3$ and $1/2$ States on Various Lattices
• Higher-order topology protected by latent crystalline symmetries
• Berry-dipole Semimetals
• Interacting Local Topological Markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states
• Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity
• Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter
• Yang-Lee Zeros in Quantum Phase Transition: An Entanglement Perspective
• Mesoscopic conductance fluctuations and noise in disordered Majorana wires
• Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays
• Soft topological modes protected by symmetry in rigid mechanical metamaterials
• The Geometry of (non-Abelian) Landau levels
• Unconventional topological transitions in a self-organized magnetic ladder
• Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models
• Counting Majorana bound states using complex momenta
• Proximity effects of vortices in neutron ${}^3{P}_2$ superfluids in neutron stars: Vortex core transitions and covalent bonding of vortex molecules
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Topological crystalline protection in a photonic system
• Magnetic tilting and emergent Majorana spin connection in topological superconductors
• Predicting topological materials: symmetry-based indicator theories and beyond
• Coexistence of 1D and 2D topology and genesis of Dirac cones in the chiral Aubry-André model
• Coherent single-spin electron resonance spectroscopy manifested at an exceptional-point singularity in a doped polyacetylene
• Even spheres as joint spectra of matrix models
• Read-Green points and level crossings in XXZ central spin models and $p_x+i{p}_y$ topological superconductors
• Defect bulk-boundary correspondence of topological skyrmion phases of matter
• Gapless Fermionic Systems as Phase-space Topological Insulators: Non-perturbative Results from Anomalies
• Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems
• 4D beyond-cohomology topological phase protected by $C_2$ symmetry and its boundary theories
• Dirac Fermions and Topological Phases in Magnetic Topological Insulator Films
• Rigidity of topological invariants to symmetry breakings
• Universal Wilson Loop Bound of Quantum Geometry
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Semiclassical electron transport at the edge of a 2D topological insulator: Interplay of protected and unprotected modes
• Finite Size Scaling at the Topological Transition: Bilinear-Biquadratic Spin-1 Chain
• Superlattice platform for chiral superconductivity with tuneable and high Chern numbers
• Gate-tunable imbalanced Kane-Mele model in encapsulated bilayer jacutingaite
• Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice
• The tenfold way redux: Fermionic systems with $N$-body interactions
• Quantized electromagnetic response of three-dimensional chiral topological insulators
• BerryEasy: A GPU enabled python package for diagnosis of nth-order and spin-resolved topology in the presence of fields and effects
• Gappability Index for Quantum Many-Body Systems
• Symmetry-Resolved Entanglement of $C_2$-symmetric Topological Insulators
• Effective response theory for zero energy Majorana bound states in three spatial dimensions
• Topological gapless points in superconductors: From the viewpoint of symmetry
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Controlling Majorana hybridization in magnetic chain-superconductor systems
• Selection Rule for Topological Amplifiers in Bogoliubov de Gennes Systems
• Topological Modes Protected by Chiral and Two-Fold Rotational Symmetry in a Spring-Mass Model with a Lieb Lattice Structure
• Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice
• Rigorous analysis of the topologically protected edge states in the quantum spin Hall phase of the armchair ribbon geometry
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Charge conservation protected topological phases
• Transport in topological insulator nanowires
• Quantum geometry of bosonic Bogoliubov quasiparticles
• Edge-dependent anomalous topology in synthetic photonic lattices subject to discrete step walks
• Effect of incommensurate potential on nodal-link semimetals
• Anomalous Hall effect from a non-Hermitian viewpoint
• Analytical and semianalytical tools to determine the topological character of Shiba chains
• Discovery of topological metamaterials by symmetry relaxation and smooth topological indicators
• Almost Strong Zero Modes at Finite Temperature
• Rotationally invariant ensembles of integrable matrices
• Interaction-Driven Topological Switch in a $P$-Band Honeycomb Lattice
• Hall and spin Hall viscosity ratio in 2d topological insulators
• Pressure-Driven Topological Phase Transition in the Yb Chalcogenides YbO and YbS
• Green's Function Method for Line Defects and Gapless Modes in Topological Insulators : Beyond Semiclassical Approach
• Suppression of Shot Noise in a Dirty Marginal Fermi Liquid
• Fermionic Symmetry Protected Topological Phase Induced by Interactions
• Electronic polarization in non-Bloch band theory
• Topological dualities via tensor networks
• Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems
• Holographic Wilson Loops, Dielectric Interfaces, and Topological Insulators
• Induced topological order at the boundary of 3D topological superconductors
• Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
• Parsing skin effect in a non-Hermitian spinless BHZ-like model
• Majorana-magnon interactions in topological Shiba chains
• Chern dartboard insulator: sub-Brillouin zone topology and skyrmion multipoles
• Crystal-symmetry-protected gapless vortex-line phases in superconducting Dirac semimetals
• Nontrivial gapless electronic states at the stacking faults of weak topological insulators
• Noncentrosymmetric superconductors in one dimension
• Engineering 1D topological phases on $p$-wave superconductors
• Fermion-parity switches of the ground state of Majorana billiards
• Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing
• Beyond the standard model of topological Josephson junctions: From crystalline anisotropy to finite-size and diode effects
• Chiral to helical Majorana fermion transition in a $p$-wave superconductor
• Beyond the $10$-fold way: $13$ associative $Z_2\times Z_2$-graded superdivision algebras
• Supersymmetric Free Fermions and Bosons: Locality, Symmetry and Topology
• Topological Orders with Global Gauge Anomalies
• Classical topological paramagnetism
• Andreev spectroscopy of the triplet superconductivity state in Bi/Ni bilayer system
• Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
• Topological insulator on honeycomb lattices and ribbons without inversion symmetry
• Superconductivity in quantum wires: A symmetry analysis
• Chiral topological superconducting state with Chern number $\mathcal{C}=-2$ in Pb${}_3$Bi/Ge(111)
• Gauge interactions and topological phases of matter
• Almost commuting self-adjoint matrices --- the real and self-dual cases
• On the Sign of Fermion-Mediated Interactions
• Bulk thermal transport coefficients in a quantum Hall system and the fundamental difference between thermal and charge response
• Entanglement and particle fluctuations of one-dimensional chiral topological insulators
• Grain-boundary topological superconductor
• SU(3) fermions in a three-band Graphene-like model
• Disorder induced topological phase transition in a driven Majorana chain
• Symmetry classification of typical quantum entanglement
• Topological quantum thermometry
• Multiple Andreev reflections in two-dimensional Josephson junctions with broken time-reversal symmetry
• Interaction Correction to the Magneto-Electric Polarizability of $Z_2$ Topological Insulators
• Elementary models of 3D topological insulators with chiral symmetry
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description
• Intrinsic Chern-Connes Characters for Crossed Products by ${\mathbb{Z}}^d$
• Bound states of three fermions forming symmetry-protected topological phases
• Enhancement of Superconductivity in a Dirty Marginal Fermi Liquid
• Floquet-engineered diode performance in a Majorana-quantum dot Josephson junction
• Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect
• Flat bands in condensed-matter systems -- perspective for magnetism and superconductivity
• Synthesizing Weyl semimetals in weak topological insulator and topological crystalline insulator multilayers
• Interactions and the Theta Term in One-Dimensional Gapped Systems
• Majorana modes in multiband superconducting quantum wires
• Individually tunable tunnelling coefficients in optical lattices using local periodic driving
• Topological photon pumping in quantum optical systems
• Invariance of topological indices under Hilbert space truncation
• Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model
• Weakly interacting one-dimensional topological insulators: a bosonization approach
• Symmetry-enriched Bose-Einstein condensates in spin-orbit coupled bilayer system
• Hofstadter problem in higher dimensions
• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• Entanglement Chern Number of the Kane-Mele Model with Ferromagnetism
• Interplay between intrinsic and emergent topological protection on interacting helical modes
• Chiral topological superconductivity in Josephson junction
• Continuous vibronic symmetries in Jahn-Teller models
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Interacting SPT phases are not Morita invariant
• On Anderson Localization and Chiral Anomaly in Disordered Time-Reversal Invariant Weyl Semimetals: Nonperturbative and Berry Phase Effects
• Quantum phase transitions and a disorder-based filter in a Floquet system
• Machine learning of mirror skin effects in the presence of disorder
• Supercurrent-Induced Weyl Superconductivity
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle
• Exact correlations in topological quantum chains
• Symmetric Fermi projections and Kitaev's table: topological phases of matter in low dimensions
• Strong and Weak Three-Dimensional Topological Insulators Probed by Surface Science Methods
• Topological properties of magnetically ordered heavy-fermion systems in the presence of mirror symmetry
• Majorana multipole response with magnetic point group symmetry
• Solvable 2D superconductors with l-wave pairing
• Disordered Graphene Ribbons as Topological Multicritical Systems
• Tailoring topological states in silicene using different halogen-passivated Si(111) substrates
• Classifying parafermionic gapped phases using matrix product states
• Microwave signatures of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$ fractional Josephson effects
• Visualising the connection between edge states and the mobility edge in adiabatic and non-adiabatic topological charge transport
• Topological Phase Transition in a Molecular Hamiltonian with Symmetry and Pseudo-Symmetry, Studied through Quantum, Semi-Quantum and Classical Models
• Precise determination of critical points of topological phase transitions via shift current in two-dimensional inversion asymmetric insulators
• Exciton Berryology
• Detecting non-Abelian statistics of topological states on a chain of superconducting circuits
• Adiabatic charge transport in extended SSH models
• Topological, multi-mode amplification induced by non-reciprocal, long-range dissipative couplings
• Solvable lattice model for (2+1)D bosonic topological insulator
• A search for correlation-induced adiabatic paths between distinct topological insulators
• The Future of the Correlated Electron Problem
• Scaling of critical wavefunctions at topological Anderson transitions in 1D
• Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries
• Hong-Ou-Mandel Interference in a temporal-average-inversion-symmetric chain
• Topological magnetoelectric pump in three dimensions
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems
• Fate of symmetry protected coherence in open quantum system
• The cohomology invariant for class DIII topological insulators
• Equivalence of topological mirror and chiral superconductivity in one dimension
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. II. Topological classification
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Punctured-Chern topological invariants for semi-metallic bandstructures
• $K$-theory classification of Wannier localizability and detachable topological boundary states
• Entanglement in topological systems
• Quasiperiodicity protects quantized transport in disordered systems without gaps
• Boundary and defect criticality in topological insulators and superconductors
• Correlated Zak insulator in organic antiferromagnets
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Multifractal Properties of Tribonacci Chains
• Topological insulators on fractal lattices: A general principle of construction
• Quantized thermal and spin transports of dirty planar topological superconductors
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Bound states and local topological phase diagram of classical impurity spins coupled to a Chern insulator
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Type-II topological phase transitions of topological skyrmion phases
• Majorana bound state of a Bogoliubov-de Gennes-Dirac Hamiltonian in arbitrary dimensions
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Quantized topological phases beyond square lattices in Floquet synthetic dimensions
• Topological strings linking with quasi-particle exchange in superconducting Dirac semimetals
• Designing nontrivial one-dimensional Floquet topological phases using a spin-1/2 double-kicked rotor
• Mirror-symmetry protected higher-order topological zero-frequency boundary and corner modes in Maxwell lattices
• Dimensional reduction and scattering formulation for even topological invariants
• Dynamical Chiral Symmetry and Symmetry-Class Conversion in Floquet Topological Insulators
• Symmetry-Protected Solitons and Bulk-Boundary Correspondence in Generalized Jackiw-Rebbi Models
• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• Topological extension including quantum jump
• Selective branching, quenching, and converting of topological modes
• Signatures of topological quantum phase transitions in driven and dissipative qubit-arrays
• State Transfer in Latent-Symmetric Networks
• On the detectability of paraparticles beyond bosons and fermions
• Universal properties of boundary and interface charges in multichannel one-dimensional continuum models
• Majorana zero modes in a quantum wire platform without Rashba spin-orbit coupling
• An elementary proof and detailed investigation of the bulk-boundary correspondence in the generic two-band model of Chern insulators
• Signatures of surface Majorana modes in the magnetic response of topological superconductors
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants
• Complete characterization of spin chains with two Ising symmetries
• Brane order and quantum magnetism in modulated anisotropic ladders
• Instability of Majorana states in Shiba chains due to leakage into a topological substrate
• Takagi Topological Insulator on the Honeycomb Lattice
• Topology of ultra-localized insulators and superconductors
• Hermitian and non-Hermitian topology in active matter
• Topological quantum phase transition in strongly correlated Kondo insulators in 1D
• Two parameter scaling in the crossover from symmetry class BDI to AI
• Topological phases in discrete stochastic systems
• Finite-temperature topological invariant for higher-order topological insulators
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Topological Superconductor from the Quantum Hall Phase: Effective Field Theory Description
• Dynamics of Anderson localization in disordered wires
• Effective models for dense vortex lattices in the Kitaev honeycomb model
• Interband excitations in the 1D limit of two-band fractional Chern insulators
• Topological phases of many-body non-Hermitian systems
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down
• Intrinsic (Axion) Statistical Topological Insulator
• A linear algebra-based approach to understanding the relation between the winding number and zero-energy edge states
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Quantum-critical dynamics of a Josephson junction at the topological transition
• General response theory of topologically stable Fermi points and its implications for disordered cases
• Field-Programmable Topological Array: Framework and Case-Studies
• Random Quantum Circuits with Time-Reversal Symmetry
• Representation-protected topology of spin-singlet $s$-wave superconductors
• Ever-present Majorana bound state in a generic one-dimensional superconductor with odd number of Fermi surfaces
• Hall effect of ferro/antiferromagnetic wallpaper fermions
• Field-driven band asymmetry and non-reciprocal transport in a helimagnet
• On the Emergent Dynamics of Fermions in Curved Spacetime
• Direct topological insulator transitions in three dimensions are destabilized by non-perturbative effects of disorder
• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
• Critical Filaments and Superconductivity in Quasiperiodic Twisted Bilayer Graphene
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Quantum Hall criticality in an amorphous Chern insulator
• Unremovable linked nodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekulé texture
• Effective field theory of topological insulator and the Foldy-Wouthuysen transformation
• Solitons induced by an in-plane magnetic field in rhombohedral multilayer graphene
• Kibble-Zurek mechanism and errors of gapped quantum phases
• Hybrid symmetry class topological insulators
• Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model
• Discrete Quantum Geometry and Intrinsic Spin Hall Effect
• Unconventional Topological Insulators from Extended Topological Band Degeneracies
• Fragile topology in nodal-line semimetal superconductors
• Cold atoms meet lattice gauge theory
• Quantum Restored Symmetry Protected Topological Phases
• Topological end states in two-orbital double-exchange model for colossal magnetoresistive manganites
• Exceptional Points, Bulk-Boundary Correspondence, and Entanglement Properties for a Dimerized Hatano-Nelson Model with Staggered Potentials
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Superconductivity in doped planar Dirac insulators: A renormalization group study
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Extended Dynamical Symmetries of Landau Levels in Higher Dimensions
• Non-hermitian topology and entanglement in an optomechanical superlattice
• Topological insulators and geometry of vector bundles
• Arboreal Obstructed Atomic Insulating and Metallic Phases of Fermions
• Gapless Topological Peierls-like instabilities in more than one dimension
• Majorana modes in helical altermagnet without net magnetism and spin-orbit coupling
• Making s-wave superconductors topological with magnetic field
• Twisted Nodal Superconductors
• Generic reduction theory for Fermi sea topology in metallic systems
• Non-Hermitian Hopf insulators
• Emergent fractals in dirty topological crystals
• Breakdown of Bulk-Radiation Correspondence in Radiative Photonic Lattices
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Surface theory of a second-order topological insulator beyond the Dirac approximation
• C*-framework for higher-order bulk-boundary correspondences
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Floquet Möbius topological insulators
• Spin Geometry and Some Applications
• Modulating Hamiltonian Approach to Quantum Many-Body Systems and Crystalline Topological Phases Protected by Generalized Magnetic Translations
• Critical phase boundary and finite-size fluctuations in Su-Schrieffer-Heeger model with random inter-cell couplings
• Photocurrent and photoconductance of an helical edge state
• Quantized and maximum entanglement from sublattice symmetry
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Towards electrical domain-wall control in polyacetylene-based electronic nanodevices
• A non-Hermitian Su-Schrieffer-Heeger model with the energy levels of free parafermions
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Topological Fulde-Ferrell Superfluids in Triangular Lattices
• ${}^3$He-R: A Topological $s^{\pm }$ Superfluid with Triplet Pairing
• Extensions of Lattice Groups, Gerbes and Chiral Fermions on a Torus
• Perfectly localized Majorana corner modes in fermionic lattices
• $Z_2\times Z_2$ symmetry and $Z_4$ Berry phase of bosonic ladder
• Gauge Dynamics and Topological Insulators
• Geometric and computational aspects of chiral topological quantum matter
• Nodal lines and boundary modes in topological Dirac semimetals with magnetism
• Time-dependent driving and topological protection in the fractional Josephson effect
• Unified scattering approach to Josephson current and thermal noise in BCS and topological superconducting junctions
• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
• On braid statistics versus parastatistics
• The $Z_2$ Classification of Dimensional Reduced Hopf Insulators
• Effect of Disorder on the Conductance of (non-) Topological SN Junctions
• Berry curvature and quantum metric in copper-substituted lead phosphate apatite
• Anomalous Linear and Quadratic Nodeless Surface Dirac Cones in Three-Dimensional Dirac Semimetals
• Hopf Semimetals
• Redundant string symmetry-based error correction: Demonstrations on quantum devices
• Topological Properties of Single-Particle States Decaying into a Continuum due to Interaction
• Three-dimensional $\mathbb{Z}$ topological insulators without reflection symmetry
• Stability of the X-Y-phase of the two-dimensional C4 point group insulator
• PT-symmetric Non-Hermitian Hopf Metal
• Robust quantisation of circular photogalvanic effect in multiplicative topological semimetals
• Topological Phase Transitions with Zero Indirect Band Gap
• Inducing ${\mathbb{Z}}_2$ Topology in Twisted Nodal Superconductors
• Neutrino zeromodes on electroweak strings in light of topological insulators
• Brick Wall Quantum Circuits with Global Fermionic Symmetry
• Fractons on the edge
• A Unified Construction of Skyrme-type Non-linear sigma Models via The Higher Dimensional Landau Models
• Re-entrant topological order in strongly correlated nanowire due to Rashba spin-orbit coupling
• Symmetry breaking, strain solitons and mechanical edge modes in monolayer antimony
• Topological bosonic Bogoliubov excitations with sublattice symmetry
• Bloch and Bethe ansatze for the Harper model: A butterfly with a boundary
• Bulk versus surface: Nonuniversal partitioning of the topological magnetoelectric effect
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes
• Nonreciprocal Equilibrium Josephson Effect of Arbitrary Periodicity from Poor Man's Majorana Zero Modes
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping
• Topological Insulators at Strong Disorder
• TopologicalNumbers.jl: A Julia package for topological number computation
• Scattering description of edge states in Aharonov-Bohm triangle chains
• Long-range Coulomb interaction effects on the surface Dirac electron system of a three-dimensional topological insulator
• Classification of spin Hall effect in two-dimensional systems
• Obstructed Atomic Insulators and Superfluids of Fermions Coupled to ${\mathbb{Z}}_2$ Gauge Fields
• Characterization of the 2D Su-Schrieffer-Heeger Model with Second-Nearest-Neighbor Interactions
• Solitons in binary compounds with stacked two-dimensional honeycomb lattices
• Hidden chiral symmetries in BDI multichannel Kitaev chains
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Inversion-symmetric Electron Gases as New Platforms for Topological Planar Josephson Junctions
• Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology
• SUSY QED with Lorentz-asymmetric fermionic matter and a glance at the electron's EDM
• Superconductivity in three-dimensional interacting doped topological insulators
• Topological quantum slinky motion in resonant extended Bose-Hubbard model
• Distinguishing dynamical quantum criticality through local fidelity distances
• Crystalline finite-size topology
• Emergent topological phases in an extended Su-Schrieffer-Heeger model with Rashba spin-orbit interaction, higher order hopping and domain wall
• Modular Anomalies in (2+1) and (3+1)-D Edge Theories
• Symmetry classification correspondence between quadratic Lindbladians and their steady states
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Disorder driven topological phase transitions in 1D mechanical quasicrystals
• Impact of Boundary Conditions on the Double-Kicked Quantum Rotor
• A ${\mathbb{Z}}_2$ invariant for chiral and particle-hole symmetric topological chains
• Intrinsic non-Hermitian topological phases
• Non-Abelian interference of topological edge states
• Instanton effects in lattice models of bosonic symmetry-protected topological states
• Cartesian Nodal Lines and Magnetic Kramers Weyl Nodes in Spin-Split Antiferromagnets
• Subgap states and quantum phase transitions in one-dimensional superconductor-ferromagnetic insulator heterostructures
• Euler band topology in superfluids and superconductors
• Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders
• Network model for magnetic higher-order topological phases
• Fermi arc criterion for surface Majorana modes in superconducting time-reversal symmetric Weyl semimetals
• Higher order topology in a Creutz ladder
• Topology vs localization in synthetic dimensions
• Quantum matrix geometry in the lowest Landau level and higher Landau levels
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Robust quantized thermal conductance of Majorana floating edge bands in d-wave superconductors
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Localized interfacial Phonon Modes at the Electronic Axion Domain Wall
• A ${\mathbb{Z}}_2$-Topological Index for Quasi-Free Fermions
• Regularized universal topological markers for Dirac systems
• Superfluid Stiffness and Josephson Quantum Capacitance: Adiabatic Approach and Topological Effects
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Intrinsic emergence of Majorana modes in Luttinger j=3/2 systems
• Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors
• Transgression field theory at the interface of topological insulators
• Quantum Fractality on the Surface of Topological Insulators
• Microscopic origin of scalar potential induced topological transition in massive Dirac fermions and scalar Hall effect
• Weakly Anisotropic Noncentrosymmetric Superconductors with Radial Line Nodes and Thermodynamical Anomalies
• First Order Topological Phase Transitions and Disorder Induced Majorana Modes in Interacting Fermion Chains
• Symmetry and Topology of Monitored Quantum Dynamics
• Quantum theory of fractional topological pumping of lattice solitons
• Misconceptions on Effective Field Theories and spontaneous symmetry breaking: Response to Ellis' article
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• Universal Broadening of Zero Modes: A General Framework and Identification
• Quantitative measure of topological protection in Floquet systems through the spectral localizer
• Refined Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum
• Reentrant topology and reverse pumping in a quasiperiodic flux ladder
• Topological Phase Transitions and Edge-State Transfer in Time-Multiplexed Quantum Walks
• Theory of quantum spin-Hall topological lasers
• Real-time evolution and quantized charge pumping in magnetic Weyl semimetals
• Possible Chiral Topological Superconductivity in CrO${}_2$ bilayers
• Topological Characterization of Kitaev Spin Nanoribbons with Ordered Flux Configurations
• Valley- and Orbital-Controlled 2D Chern Insulators Without Spin-orbit Interaction
• The analytically tractable zoo of similarity-induced exceptional structures
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors
• Strictly one dimensional behavior emerging from dispersive two dimensional system: implications on metallic nanowires on semiconducting substrates
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
• Hofstadter Butterflies in Topological Insulators
• Fourth-Order Topological Insulator via Dimensional Reduction
• Quantized single-particle Thouless pump induced by topology transfer from a Chern insulator at finite temperature
• Coarse geometric approach to topological phases: Invariants from real-space representations
• Cyclic cocycles and quantized pairings in materials science
• Family of multilayer graphene superconductors with tunable chirality: Momentum-space vortices nucleated by a ring of Berry curvature
• Topological phase states of the SU(3) QCD
• Weyl semimetals and spin${}^c$ cobordism
• Theory of Hofstadter Superconductors
• Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Magnetic order and transport in a spin-fermion model on a superlattice
• Topological junctions for one-dimensional systems
• Topological states of generalized dissipative Majorana wires
• A minimal tensor network beyond free fermions
• Classification of topological insulators and superconductors with multiple order-two point group symmetries
• Chirality reversal at finite magnetic impurity strength and local signatures of a topological phase transition
• Josephson effects between the Kitaev ladder superconductors
• Dimensional crossover of class D real-space topological invariants
• A Universal Chern Model on Arbitrary Triangulations
• Band rearrangement through the 3D-Dirac equation with boundary conditions, and the corresponding topological change
• Kaluza-Klein Reduction of the 6 Dimensional \\ Dirac Equation on ${\mathbb{S}}^3\cong SU(2)$ and \\ Non-abelian Topological Insulators
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Combined spontaneous symmetry-breaking and symmetry-protected topological order from cluster charge interaction
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions
• Effect of Uncorrelated On-site Scalar Potential and Mass Disorder on Transport of Two-Dimensional Dirac Fermions
• Identification of the Majorana edge modes in tight-binding systems based on the Krylov method
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• Symmetry-protected topological wire in a topological vacuum
• Equatorial magnetoplasma waves
• Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry
• Dynamical Symmetry Indicators for Floquet Crystals
• Topological phases of monolayer and bilayer depleted Lieb lattices
• From orthogonal link to phase vortex in generalized dynamical Hopf insulators
• Topology with broken parity-time symmetry
• Floquet topological phases with high Chern numbers in a periodically driven extended Su-Schrieffer-Heeger model
• Coupled-wire construction of non-Abelian higher-order topological phases
• Topological superconductivity and superconducting diode effect mediated via unconventional magnet and Ising spin-orbit coupling
• Theory of Berry Singularity Markers: Diagnosing Topological Phase Transitions via Lock-In Tomography
• Multiplicative Chern insulator
• Topological phases of bosons with local parity coupling on a dimerized lattice
• Polarization-dependent topology in quantum emitter chains
• Surface topological quantum criticality: Conformal manifolds and Discrete Strong Coupling Fixed Points
• Simulating monitoring-induced topological phase transitions with small systems
• Topological Anderson insulator and reentrant topological transitions in a mosaic trimer lattice
• Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group
• Disorder-Induced Topological Phases in a Two-Dimensional Chern Insulator with Strong Magnetic Disorder
• Fluctuations of Wigner-type random matrices associated with symmetric spaces of class DIII and CI
• Analytical solutions of topological surface states in a series of lattice models
• Kernel(J) warns of false vacua
• Layer-number parity induced topological phase transition
• Winding Number Statistics for Chiral Random Matrices: Universal Correlations and Statistical Moments in the Unitary Case
• Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values
• Lattice-induced wavefunction effects on trapped superfluids
• Topological Invariant for Bosonic Bogoliubov-de Gennes Systems with Disorder
• Hidden chiral symmetry protected $\mathbb{Z}\oplus \mathbb{Z}$ topological insulators in a ladder dimer model
• Interplay of Tilt and Axion Fields in Topological Superconductors: Anisotropy in the Meissner Effect
• Tenfold Way for Holography : AdS/CFT and Beyond
• Chern insulators in two and three dimensions: A global perspective
• Three-dimensional spinless Euler insulators with rotational symmetry
• Interacting Majorana fermions in strained nodal superconductors
• Generalized symmetry enriched criticality in (3+1)d
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Exact Mappings in Condensed Matter Physics
• Hinge modes of three-dimensional Euler insulators
• Antilinear superoperator, quantum geometric invariance, and antilinear symmetry for higher-dimensional quantum systems
• Topological insulators from the perspective of non-commutative geometry and index theory
• Electrostatically-induced topological phase transitions in polyacetylene molecules
• Almost Commuting Orthogonal Matrices
• Periodic Orbit Theory Revisited in the Anisotropic Kepler Problem
• Correspondence of topological classification between quantum graph extra dimension and topological matter
• Topological bands in the continuum using Rydberg states