Topology of crystalline insulators and superconductors

Abstract

We complete a classification of topological phases and their topological defects in crystalline insulators and superconductors. We consider topological phases and defects described by non-interacting Bloch and Bogoliubov de Gennes Hamiltonians that support additional order-two spatial symmetry, besides any of ten classes of symmetries defined by time-reversal symmetry and particle-hole symmetry. The additional order-two spatial symmetry we consider is general and it includes $Z_2$ global symmetry, mirror reflection, two-fold rotation, inversion, and their magnetic point group symmetries. We find that the topological periodic table shows a novel periodicity in the number of flipped coordinates under the order-two spatial symmetry, in addition to the Bott-periodicity in the space dimensions. Various symmetry protected topological phases and gapless modes will be identified and discussed in a unified framework. We also present topological classification of symmetry protected Fermi points. The bulk classification and the surface Fermi point classification provide a novel realization of the bulk-boundary correspondence in terms of the K-theory.

arXiv comment58 pages, final version

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• Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors
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• Topological classification with additional symmetries from Clifford algebras
• Topological odd-parity superconductors
• Topological phases and surface flat bands in superconductors without inversion symmetry
• Twisted equivariant matter
• The strong side of weak topological insulators
• Topological spin-current in non-centrosymmetric superconductors
• Topological superconductivity in bilayer Rashba system
• Topological Mirror Superconductivity
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Topological Classification and Stability of Fermi Surfaces
• An Introduction to Topological Insulators
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Detecting the Majorana fermion surface state of ${}^3$He-B through spin relaxation
• Majorana Fermions and Disclinations in Topological Crystalline Superconductors
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Majorana Fermions and Exotic Surface Andreev Bound States in Topological Superconductors: Application to CuxBi2Se3
• Topological non-symmorphic crystalline insulators
• Anomalous Andreev bound state in non-centrosymmetric superconductors
• Majorana Kramers Doublets in $d_{x^2-y^2}$-wave Superconductors with Rashba Spin-Orbit Coupling
• Quantum transport and two-parameter scaling at the surface of a weak topological insulator
• Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application to Sr2RuO4
• Topological Classification of Crystalline Insulators with Point Group Symmetry
• Time-reversal invariant topological superconductivity in doped Weyl semimetals
• Spinless Topological Insulators without Time-Reversal Symmetry
• Surface density of states and topological edge states in non-centrosymmetric superconductors
• Majorana Fermions in Nodal Superconductors: Gapless Topological Phase
• Topological field theory and thermal responses of interacting topological superconductors
• Symmetry protected topological phases in non-interacting fermion systems
• Tunneling Conductance and Surface States Transition in Superconducting Topological Insulators
• Majorana bound states and non-local spin correlations in a quantum wire on an unconventional superconductor
• Cross-Correlated Responses of Topological Superconductors and Superfluids
• Equivalent topological invariants of topological insulators
• Statistical Topological Insulators
• Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number
• Topological Insulators with Commensurate Antiferromagnetism
• Topologically stable gapless phases of time-reversal invariant superconductors
• Axion topological field theory of topological superconductors
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B
• Surface spectral function in the superconducting state of a topological insulator
• From the adiabatic theorem of quantum mechanics to topological states of matter
• New class of topological superconductors protected by magnetic group symmetries
• Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Strong Anisotropy in Spin Suceptibility of Superfluid 3He-B Film Caused by Surface Bound States
• Twofold spontaneous symmetry breaking in a heavy fermion superconductor UPt${}_3$
• Non-Abelian Statistics of Axion Strings
• Symmetries, Dimensions, and Topological Insulators: the mechanism behind the face of the Bott clock
• Turning a Band Insulator Into an Exotic Superconductor
• Topological superfluid 3He-B in magnetic field and Ising variable
• Anomalous Topological Pumps and Fractional Josephson Effects
• Revealing a topological connection between stabilities of Fermi surfaces and topological insulators/superconductors
• Quantum impurity spin in Majorana edge fermions
• A Spin Triplet Superconductor UPt${}_3$
• Topological Majorana and Dirac zero modes in superconducting vortex cores
• Axionic superconductivity in three dimensional doped narrow gap semiconductors
• Classification of engineered topological superconductors
• Topological phases of quasi-one-dimensional fermionic atoms with a synthetic gauge field
• Symmetry protected Z2-quantization and quaternionic Berry connection with Kramers degeneracy
• Spin-polarized Majorana Bound States inside a Vortex Core in Topological Superconductors
• Electromagnetic and thermal responses of Z topological insulators and superconductors in odd spatial dimensions
• Mirror Majorana zero modes in spinful superconductors/superfluids -Non-Abelian braiding of integer quantum vortices-
• Majorana states and longitudinal NMR absorption in ${}^3$He-B film
• Charge Ordering and Ferroelectricity in Half-doped Manganites
• Index theorem for topological heterostructure systems
• Spectrum of bound fermion states on vortices in ${}^3$He-B

Cited by in corpus (388)

• Classification of topological quantum matter with symmetries
• Non-Hermitian Physics
• Topological superconductors: a review
• Colloquium: Topological Band Theory
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• Symmetry and Topology in Non-Hermitian Physics
• Reflection symmetric second-order topological insulators and superconductors
• Non-Hermitian Boundary Modes
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Topological classification of crystalline insulators through band structure combinatorics
• Higher-order topological insulators and superconductors protected by inversion symmetry
• All "Magic Angles" Are "Stable" Topological
• Novel Topological Phase with Zero Berry Curvature
• Hourglass Fermions
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Topological semi-metals with line nodes and drumhead surface states
• Non-Hermitian topological phenomena: A review
• Majorana Fermions and Topology in Superconductors
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Quantitative mappings between symmetry and topology in solids
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• A fractional corner anomaly reveals higher-order topology
• Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
• Anomalous helical edge states in a non-Hermitian Chern insulator
• Topological surface states in nodal superconductors
• Gauging spatial symmetries and the classification of topological crystalline phases
• Topological superconductivity in Dirac semimetals
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Are the double Fermi arcs of Dirac semimetals topologically protected?
• Topology of nonsymmorphic crystalline insulators and superconductors
• Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSb
• Unified theory of PT and CP invariant topological metals and nodal superconductors
• Rotation Anomaly and Topological Crystalline Insulators
• Lattice models with exactly solvable topological hinge and corner states
• Topological phases without crystalline counterparts
• Floquet second-order topological insulators from nonsymmorphic space-time symmetries
• Geometric approach to fragile topology beyond symmetry indicators
• Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
• Dynamical classification of topological quantum phases
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Higher-order Floquet topological phases with corner and bulk bound states
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Nonsymmorphic symmetry-required band crossings in topological semimetals
• Topological Insulators from Group Cohomology
• Topological tight-binding models from non-trivial square roots
• Interplay between electronic topology and crystal symmetry: Dislocation-line modes in topological band-insulators
• Graph Theory Data for Topological Quantum Chemistry
• Band Representations and Topological Quantum Chemistry
• Non-Hermitian second-order skin and topological modes
• Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals
• Aperiodic Weak Topological Superconductors
• Floquet topological phases protected by time glide symmetry
• Theory of interacting topological crystalline insulators
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials
• Many-body topological invariants for fermionic symmetry-protected topological phases
• Topological transport in Dirac nodal-line semimetals
• Topological correspondence between magnetic space group representations
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Topological states from topological crystals
• Su-Schrieffer-Heeger Model Inspired Acoustic Interface States and Edge States
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Superconductivity and Local Inversion-Symmetry Breaking
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Square-root higher-order topological insulator on a decorated honeycomb lattice
• Crystalline topological phases as defect networks
• Braiding Majorana corner modes in a second-order topological superconductor
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Topological Entanglement-Spectrum Crossing in Quench Dynamics
• Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Mirror winding number and helical edge modes in honeycomb lattice with hopping-energy texture
• Fragile Phases As Affine Monoids: Classification and Material Examples
• Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines
• Topological Bloch oscillations
• Classification of topological insulators and superconductors out of equilibrium
• Partial lattice defects in higher order topological insulators
• Global band topology of simple and double Dirac-point (semi-)metals
• Crystalline Nodal Topological Superconductivity and Bogolyubov Fermi Surfaces in Monolayer NbSe${}_2$
• Higher-order topological band structures
• Topological Mirror Insulators in One Dimension
• ${\mathbb{Z}}_2$ Topological Invariant for Magnon Spin Hall Systems
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Floquet higher-order topological insulators and superconductors with space-time symmetries
• Topological Materials Discovery By Large-order symmetry indicators
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• Classification of topological crystalline insulators based on representation theory
• Topological crystalline superconductivity in locally noncentrosymmetric CeRh${}_2$As${}_2$
• Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena
• Three-dimensional superconductors with hybrid higher order topology
• Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries
• Topological Crystalline Superconductivity in Locally Non-centrosymmetric Multilayer Superconductors
• Topological classification and diagnosis in magnetically ordered electronic materials
• Topologically stable gapless phases in nonsymmorphic superconductors
• Topological metals and finite-momentum superconductors
• Non-Hermitian band topology with generalized inversion symmetry
• Real-space recipes for general topological crystalline states
• Two-dimensional Shiba lattices as possible platform for crystalline topological superconductivity
• Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
• Atiyah-Hirzebruch Spectral Sequence in Band Topology: General Formalism and Topological Invariants for 230 Space Groups
• Non-Hermiticity and topological invariants of magnon Bogoliubov-de Gennes systems
• Wannier representation of Floquet topological states
• Conversion rules for Weyl points and nodal lines in topological media
• Symmetry indicators for topological superconductors
• Topological band crossings in hexagonal materials
• Topological phase transitions in multi-component superconductors
• Exceptional band touching for strongly correlated systems in equilibrium
• Topological Properties of Gapped Graphene Nanoribbons with Spatial Symmetries
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Type-II Dirac surface states in topological crystalline insulators
• Phonon-induced Floquet second-order topological phases protected by space-time symmetries
• Classification of "Real" Bloch-bundles: Topological quantum systems of type AI
• The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• Exact Higher-order Bulk-boundary Correspondence of Corner-localized States
• Majorana-Weyl crossings in topological multi-terminal junctions
• Testing Topological Protection of Edge States in Hexagonal Quantum Spin Hall Candidate Materials
• Excess charges as a probe of one-dimensional topological crystalline insulating phases
• CPT theorem and classification of topological insulators and superconductors
• Topological Crystalline Materials of $J=3/2$ Electrons: Antiperovskites, Dirac points, and High Winding Topological Superconductivity
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• Symmetry Protected Topological Superfluid ${}^3$He-B
• Möbius topological superconductivity in UPt${}_3$
• Non-Abelian Bloch oscillations in higher-order topological insulators
• Topological space-time crystal
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Quantization of Conductance Minimum and Index Theorem
• $Z_4$ Topological Superconductivity in UCoGe
• Superconducting doped topological materials
• Fragile surface zero-energy flat bands in three-dimensional chiral superconductors
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• $Z_N$ Berry Phases in Symmetry Protected Topological Phases
• Crystalline Kitaev spin liquids
• Valley-dependent Corner States in Honeycomb Photonic Crystal without Inversion Symmetry
• Hourglass semimetals with nonsymmorphic symmetries in three dimensions
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• Axion coupling in the hybrid Wannier representation
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• Paramagnetically induced gapful topological superconductors
• Optical manifestations and bounds of topological Euler class
• Surface electronic state of superconducting topological crystalline insulator
• Disorder-Induced Quantum Phase Transitions in Three-Dimensional Second-Order Topological Insulators
• Majorana Zero Modes Protected by Hopf Invariant in Topologically Trivial Superconductors
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Symmetry indicator in non-Hermitian systems
• Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice
• Topological Nonsymmorphic Crystalline Superconductors
• Synthetic Weyl Points and Chiral Anomaly in Majorana Devices with Nonstandard Andreev-Bound-State Spectra
• Amorphous topological phases protected by continuous rotation symmetry
• Layered Topological Crystalline Insulators
• Piezoelectricity and Topological Quantum Phase Transitions in Two-Dimensional Spin-Orbit Coupled Crystals with Time-Reversal Symmetry
• Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
• Faithful derivation of symmetry indicators: A case study for topological superconductors with time-reversal and inversion symmetries
• Rotation Symmetry-Protected Topological Phases of Fermions
• $N$-band Hopf insulator
• General Theory of Momentum-Space Nonsymmorphic Symmetry
• Higher-order topological insulators in a magnetic field
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• Topological continuum charges of acoustic phonons in 2D
• Quantum dynamical characterization and simulation of topological phases with high-order band inversion surfaces
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Correlation effects on topological crystalline insulators
• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors
• Anisotropic magnetic responses of topological crystalline superconductors
• Majorana multipole response of topological superconductors
• Symmetry-enforced band crossings in trigonal materials: Accordion states and Weyl nodal lines
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• Fate of Majorana modes in ${\mathrm{CeCoIn}}_5$/${\mathrm{YbCoIn}}_5$ superlattices -a test bed for reduction of topological classification-
• Noncrystalline topological superconductors
• Nodal Andreev Spectra in Multi-Majorana Three-Terminal Josephson Junctions
• Generalized Berry phase for a bosonic Bogoliubov system with exceptional points
• Topology invisible to eigenvalues in obstructed atomic insulators
• One-dimensional topological metal
• Phase transitions of non-Abelian charged nodal links in a spring-mass system
• No-go theorem for topological insulators and sure-fire recipe for Chern insulators
• Topology and symmetry of surface Majorana arcs in cyclic superconductors
• Topological invariants to characterize universality of boundary charge in one-dimensionalinsulators beyond symmetry constraints
• Proximity-induced superconductivity and quantum interference in topological crystalline insulator SnTe thin film devices
• Magnetic order on a topological insulator surface with warping and proximity-induced superconductivity
• Multiple band-crossings and Fermi surface topology: role of double nonsymmorphic symmetries in MnP-type crystal structures
• Generation of higher-order topological insulators using periodic driving
• Landau Levels of the Euler Class Topology
• Quadrupole spin polarization as signature of second-order topological superconductors
• Embedded Topological Insulators
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• $AbInitio$ Simulation of Non-Abelian Braiding Statistics in Topological Superconductors
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Surface charge theorem and topological constraints for edge states: An analytical study of one-dimensional nearest-neighbor tight-binding models
• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
• Theory of polarization textures in crystal supercells
• Novel ${\mathbb{Z}}_2$-topological metals and semimetals
• Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators
• Topological phases in odd-legs frustrated synthetic ladders
• Dirac surface states in magnonic analogs of topological crystalline insulators
• Projected Topological Branes
• Magnetoelectrically-Tunable Andreev-Bound-State Spectra and Spin Polarization in P-Wave Josephson Junctions
• Space group constraints on weak indices in topological insulators
• Topological insulators in the NaCaBi family with large SOC gaps
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Universal Relation among Many-Body Chern Number, Rotation Symmetry, and Filling
• Possible Realization of Topological Crystalline Superconductivity with Time-Reversal Symmetry in UTe2
• Double Majorana vortex zero modes in superconducting topological crystalline insulators with surface rotation anomaly
• Quantum anomalous Hall insulator in ionic Rashba lattice of correlated electrons
• Geometric Criterion for Solvability of Lattice Spin Systems
• Interplay of topology and interactions in quantum Hall topological insulators: U(1) symmetry, tunable Luttinger liquid, and interaction-induced phase transitions
• Classification of crystalline topological semimetals with an application to Na${}_3$Bi
• Boundary edge networks induced by bulk topology
• Topological properties of a generalized spin-orbit-coupled Su-Schrieffer-Heeger model
• Symmetry protected vortex bound state in superfluid ${}^3$He B-phase
• New types of topological superconductors under local magnetic symmetries
• Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions
• A gap-protected zero-Hall effect state in the quantum limit of the nonsymmorphic metal KHgSb
• Microscopic description of axisymmetric vortices in ${}^3{P}_2$ superfluids
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Odd-frequency pairing and Ising spin susceptibility in time-reversal invariant superfluids and superconductors
• Topological Mott insulator in the odd-integer filled Anderson lattice model with Hatsugai-Kohmoto interactions
• Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors
• Manipulation of Majorana Kramers Qubit and its Tolerance in Time-Reversal-Invariant Topological Superconductor
• Catalog of noninteracting tight-binding models with two energy bands in one dimension
• Novel topological insulators from crystalline symmetries
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor
• Embedded Topological Semimetals
• Majorana multipole response: General theory and application to wallpaper groups
• Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry
• Effective field theories of topological crystalline insulators and topological crystals
• Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice
• Topology in time-reversal symmetric crystals
• Prediction of Topological Crystalline Insulator and Topological Phase Transitions in Two-dimensional PbTe Films
• Topological d-wave superconductivity in two dimensions
• Topological classification of intrinsic 3D superconductors using anomalous surface construction
• Non-Abelian Half-Quantum Vortices in ${}^3{P}_2$ Topological Superfluids
• Two-dimensional non-Hermitian topological phases induced by asymmetric hopping in a one-dimensional superlattice
• Rational boundary charge in one-dimensional systems with interaction and disorder
• Nonsymmorphic symmetry protected node-line semimetal in the trigonal YH3
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Magnetic Response of Majorana Kramers Pairs Protected by Z2 Invariants
• Symmetry conditions of a nodal superconductor for generating robust flat-band Andreev bound states at its dirty surface
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Topologically distinct atomic insulators
• Spin, orbital and topological order in models of strongly correlated electrons
• Symmetry-protected topological phase transition in one-dimensional Kondo lattice and its realization with ultracold atoms
• Trapping Majorana Zero Modes in Vortices of Magnetic Texture Crystals Coupled to Nodal Superconductors
• Ground-state atlas of a three-dimensional semimetal in the quantum limit
• Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
• Generic phase diagram for Weyl superconductivity in mirror-symmetric superconductors
• Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines
• Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Simulating Floquet topological phases in static systems
• Filling-enforced Dirac loops and their evolutions under various perturbations
• Approximate symmetries and conservation laws in topological insulators and associated $\mathbb{Z}$-invariants
• Unconventional Majorana fermions on the surface of topological superconductors protected by rotational symmetry
• Hidden Symmetry Decoupling of Majorana Fermions
• Self-localized topological states in three dimensions
• Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes
• Anomalous geometric transport signatures of topological Euler class
• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Higher-order topological superconductivity in a topological metal 1T${}^{\prime }$-MoTe${}_2$
• Revealing the spatial nature of sublattice symmetry
• Disorder-induced topology in quench dynamics
• Transverse profile and 3D spin canting of a Majorana state in carbon nanotubes
• Topology of chalcogen chains
• Exact projected entangled pair ground states with topological Euler invariant
• Larkin-Ovchinnikov state of superconducting Weyl metals: Fundamental differences between pairings restricted and extended in the $\text{k}$-space
• Protected Gapless Edge States In Trivial Topology
• Higher-order topological corner states induced solely by onsite potentials with mirror symmetry
• Electric Multipoles of Double Majorana Kramers Pairs
• Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries
• Anisotropic paramagnetic response of topological Majorana surface states in the superconductor ${\text{UTe}}_2$
• 4D beyond-cohomology topological phase protected by $C_2$ symmetry and its boundary theories
• Spin-Orbit Coupling and Topological States in $F=\frac{3}{2}$ Cold Fermi Gas
• Anomalous Crystal Shapes of Topological Crystalline Insulators
• Surface-dependent Majorana vortex phases in topological crystalline insulators
• Symmetry classes of dissipative topological insulators with edge dark state
• Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice
• Crystal-symmetry-protected gapless vortex-line phases in superconducting Dirac semimetals
• Nontrivial gapless electronic states at the stacking faults of weak topological insulators
• Chiral to helical Majorana fermion transition in a $p$-wave superconductor
• Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
• Optical signatures of Euler superconductors
• Second-order topology and supersymmetry in two-dimensional topological insulators
• Interacting topological phases in thin films of topological mirror Kondo insulators
• Additive rule of real and reciprocal space topologies at disclinations
• Dynamical Majorana Ising spin response in a topological superconductor-magnet hybrid by microwave irradiation
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Unconventional hybrid-order topological insulators
• Higher-order topological superconductor phases in a multilayer system
• Second Euler number in four dimensional synthetic matter
• Entanglement Chern Number of the Kane-Mele Model with Ferromagnetism
• Synthesizing Weyl semimetals in weak topological insulator and topological crystalline insulator multilayers
• Majorana modes in multiband superconducting quantum wires
• Dual topological insulator with mirror symmetry protected helical edge states
• Flow of unitary matrices: Real-space winding numbers in one and three dimensions
• Superconducting Correlations in the One-Dimensional Kondo Lattice Models under Magnetic Fields
• Topological Aspects of Matters and Langlands Program
• Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Renormalization approach to the analysis and design of Hermitian and non-Hermitian interfaces
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Quantized thermal and spin transports of dirty planar topological superconductors
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• General corner charge formulas in various tetrahedral and cubic space groups
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• Majorana multipole response with magnetic point group symmetry
• Topological insulators on fractal lattices: A general principle of construction
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• From orthosymplectic structure to super topological matter
• Observation of trapped fractional charge and topological states at disclination defects in higher-order topological insulators
• Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator
• Theory of fractional corner charges in cylindrical crystal shapes
• Topological Micro-Electro-Mechanical Systems
• Projective Spacetime Symmetry of Spacetime Crystals
• Boundary states in the chiral symmetric systems with a spatial symmetry
• Homotopy invariant in time-reversal and twofold rotation symmetric systems
• Hedgehog spin texture and competing orders associated with strains on the surface of a topological crystalline insulator
• Two-dimensional flat band on the (011) surface of UTe${}_2$: Implication for STM measurements with a superconducting tip
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Controlling topology through targeted composite symmetry manipulation in magnetic systems
• Takagi Topological Insulator on the Honeycomb Lattice
• Dynamic melting and condensation of topological dislocation modes
• Topological nonsymmorphic insulator versus Dirac semimetal in KZnBi
• General response theory of topologically stable Fermi points and its implications for disordered cases
• Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation
• Hybrid symmetry class topological insulators
• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• Selective branching, quenching, and converting of topological modes
• Mirror-protected Majorana zero modes in $f$-wave multilayer graphene superconductors
• Topological $d$-wave Superconductivity and Nodal Line-Arc Intersections in Weyl Semimetals
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Modulating Hamiltonian Approach to Quantum Many-Body Systems and Crystalline Topological Phases Protected by Generalized Magnetic Translations
• Topological Spectral Bands with Frieze Groups
• Tunable zero-energy Dirac and Luttinger nodes in a two-dimensional topological superconductor
• Interaction-driven phase transition in one dimensional mirror-symmetry protected topological insulator
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Magnon-mediated superconductivity on ferromagnetic wallpaper fermions
• Artificial topological insulator realized in a two-terminal Josephson junction with Rashba spin-orbit interaction
• Generic reduction theory for Fermi sea topology in metallic systems
• Phase diagrams of superconducting topological surface states
• Artificial oxide heterostructures with non-trivial topology
• Stability of the X-Y-phase of the two-dimensional C4 point group insulator
• Intrinsic non-Hermitian topological phases
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges
• Unconventional Pairings and Radial Line Nodes in Inversion Symmetry Broken Superconductors
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• A Study of Curvature Theory for Different Symmetry Classes of Hamiltonian
• Nuclear spin relaxation rate of nonunitary Dirac and Weyl superconductors
• Isotropic 3D topological phases with broken time reversal symmetry
• Tuning the topology of $p$-wave superconductivity in an analytically solvable two-band model
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Engineering Helical Superconductors with Multiple Majorana Kramers Pairs via Higher-Order Rashba Spin-Orbit Coupling
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Symmetry-protected gates of Majorana qubits in a high-$T_c$ superconductor platform
• Coherence Effects of Caroli-de Gennes-Matricon Modes in Nodal Topological Superconductors
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Proximity-Induced Superconductivity in a Topological Crystalline Insulator
• Classification of topological insulators and superconductors with multiple order-two point group symmetries
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems
• Symmetry-protected topological wire in a topological vacuum
• Orbital magnetization reveals multiband topology
• Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values
• Theory of Hofstadter Superconductors
• Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups
• Dynamical Symmetry Indicators for Floquet Crystals
• Three-dimensional spinless Euler insulators with rotational symmetry
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Nodal Line Topological Superfluid and Multiply Protected Majorana Fermi Arc in a Three-Dimensional Time-Reversal-Invariant Superfluid Model