Topological Defects and Gapless Modes in Insulators and Superconductors

Abstract

We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H(k,r) that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified, and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions and helical Majorana fermions, as well as zero dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes.

arXiv comment27 pages, 15 figures, Published version

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• Time-reversal invariant finite-size topology
• Non-magnetic defects in the bulk of two-dimensional topological insulators
• Electron Correlation Effects on Topological Phases
• Topological skyrmion phases of matter
• Topologically invisible defects in chiral mirror lattices
• Competing Adiabatic Thouless Pumps in Enlarged Parameter Spaces
• Coupled Wire Models of Interacting Dirac Nodal Superconductors
• Out of equilibrium chiral higher order topological insulator on a $\pi$-flux square lattice
• Dual topological superconducting states in the layered titanium-based oxypnictide superconductor BaTi${}_2$Sb${}_2$O
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Proximity-induced quasi-one-dimensional superconducting quantum anomalous Hall state: a promising scalable top-down approach towards localized Majorana modes
• Revisiting (higher order and crystalline) topology in old models of lead telluride
• Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes
• Generalized Thouless Pumps in 1+1-dimensional Interacting Fermionic Systems
• Defects in Graphene : A Topological Description
• Magnetic Flux Response of Non-Hermitian Topological Phases
• Two-dimensional Dirac fermions in a mass superlattice
• Anomalous second-order skin modes in Floquet non-Hermitian systems
• Revealing the spatial nature of sublattice symmetry
• Observation of in-gap states in a two-dimensional CrI2/NbSe2 heterostructure
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Topological quantum transition driven by charge-phonon coupling in the Haldane Chern insulator
• Majorana stripe order on the surface of a three-dimensional topological insulator
• Electric Polarization in Inhomogeneous Crystals
• Mechanisms for Magnetic Skyrmion Catalysis and Topological Superconductivity
• Topological Quantum Criticality in Superfluids and Superconductors: Surface criticality, Thermal properties, and Lifshitz Majorana fields
• Topological Wannier cycles for the bulk and edges
• Skyrmion quantum numbers and quantized pumping in two dimensional topological chiral magnets
• SPT 2-Channel Kondo Model in the Structure of Normal Metal/Quantum Dot/DIII-class Topological Superconductor
• Realizing Corner States in Artificial Crystals Based on Topological Spin Textures
• Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity
• Band engineering and study of disorder using topology in compact high kinetic inductance cavity arrays
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Counting Majorana bound states using complex momenta
• Protection of the surface states in topological insulators: Berry phase perspective
• Unconventional topological transitions in a self-organized magnetic ladder
• Entanglement of a 3D generalization of the Kitaev model on the diamond lattice
• Magnetic chains on a triplet superconductor
• Remarks on Berry Connection in QFT, Anomalies, and Applications
• Surface spectra of Weyl semimetals through self-adjoint extensions
• Gappability Index for Quantum Many-Body Systems
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Gapless Fermionic Systems as Phase-space Topological Insulators: Non-perturbative Results from Anomalies
• Majorana Zero-modes and Topological Phases of Multi-flavored Jackiw-Rebbi model
• Universal Wilson Loop Bound of Quantum Geometry
• Crystallization in Three-Dimensions: Defect-Driven Topological Ordering and the Role of Geometrical Frustration
• Effective response theory for zero energy Majorana bound states in three spatial dimensions
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Surfaces and Slabs of Fractional Topological Insulator Heterostructures
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• The bulk-dislocation correspondence for weak topological insulators on screw-dislocated lattices
• The weak side of strong topological insulators
• Defect bulk-boundary correspondence of topological skyrmion phases of matter
• Control of Edge Currents at a Ferromagnet - Triplet Superconductor Interface by Multiple Helical Majorana Modes
• Practical new platform for interaction-enabled topological phases
• Rigidity of topological invariants to symmetry breakings
• Topological quantum criticality from multiplicative topological phases
• High critical temperature nodal superconductors as building block for time-reversal invariant topological superconductivity
• Topological Phases in Nodeless Tetragonal Superconductors
• Crystal-symmetry-protected gapless vortex-line phases in superconducting Dirac semimetals
• Robust propagating in-gap modes due to spin-orbit domain walls in graphene
• Emergent metallicity at the grain boundaries of higher-order topological insulators
• Parsing skin effect in a non-Hermitian spinless BHZ-like model
• Green's Function Method for Line Defects and Gapless Modes in Topological Insulators : Beyond Semiclassical Approach
• Higher Berry curvature from matrix product states
• Nontrivial gapless electronic states at the stacking faults of weak topological insulators
• Supersymmetric Free Fermions and Bosons: Locality, Symmetry and Topology
• Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
• Topological s-wave pairing superconductivity with spatial inhomogeneity: Mid-gap-state appearance and robustness of superconductivity
• Self-consistent study of topological superconductivity in two-dimensional quasicrystals
• Anomalous Coherence Length of Majorana Zero Modes at Vortices in Superconducting Topological Insulators
• Nested Defects on the Boundary of Topological Superconductors
• Elementary models of 3D topological insulators with chiral symmetry
• A coupled wire description of surface $ADE$ topological orders
• Topological excitations at time vortices in periodically driven systems
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• Spin Hall conductivity in Bi${}_{1-x}$Sb${}_x$ as an experimental test of bulk-boundary correspondence
• Symmetric Fermi projections and Kitaev's table: topological phases of matter in low dimensions
• Grain-boundary topological superconductor
• Entanglement and particle fluctuations of one-dimensional chiral topological insulators
• Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect
• Unconventional hybrid-order topological insulators
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• Topological Aspects of Matters and Langlands Program
• Double Majorana Vortex Flat Bands in the Topological Dirac Superconductor
• Mimicking black hole event horizons in atomic and solid-state systems
• Higher-dimensional generalizations of the Thouless charge pump
• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• Gapless state of interacting Majorana fermions in a strain-induced Landau level
• Coupled Layer Construction for Synthetic Hall Effects in Driven Systems
• Strain induced spin vortex and Majorana Kramer's pairs in doped topological insulators with nematic superconductivity
• The cohomology invariant for class DIII topological insulators
• Flow of unitary matrices: Real-space winding numbers in one and three dimensions
• The product of two independent Su-Schrieffer-Heeger chains yields a two-dimensional Chern insulator
• 4$\pi$ and 8$\pi$ dual Josephson effects induced by symmetry defects
• 1D topological chains with Majorana fermions in 2D non-topological optical lattices
• Topologically Induced Fermion Parity Flips in Superconductor Vortices
• Detrimental effects of disorder in two-dimensional time-reversal invariant topological superconductors
• Strong-coupling approach to temperature dependence of competing orders of superconductivity: Possible time-reversal symmetry breaking and nontrivial topology
• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• Superconductive proximity in a Topological Insulator slab and excitations bound to an axial vortex
• Generalized index theorem for topological superconductors with Yang-Mills-Higgs couplings
• Kondo Tunneling into a Quantum Spin Hall Insulator
• Time-reversal invariant topological skyrmion phases
• Majorana bound state of a Bogoliubov-de Gennes-Dirac Hamiltonian in arbitrary dimensions
• Layer Construction of Three-Dimensional Z2 Monopole Charge Nodal Line Semimetals and prediction of the abundant candidate materials
• Bound states and local topological phase diagram of classical impurity spins coupled to a Chern insulator
• Non-Abelian Majorana fermions in topological $s$-wave Fermi superfluids
• Topological magnonic dislocations modes
• Hybrid symmetry class topological insulators
• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• Topological strings linking with quasi-particle exchange in superconducting Dirac semimetals
• Chiral Majorana edge states in the vortex core of a $p+ip$ Fermi superfluid
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Quantum spin Hall effect in bilayer honeycomb lattices with C-type antiferromagnetic order
• Enhanced and stable spin Hall conductivity in a disordered time-reversal and inversion symmetry broken topological insulator thin film
• 3D Network Model for Strong Topological Insulator Transitions
• General response theory of topologically stable Fermi points and its implications for disordered cases
• Controlling the real-time dynamics of a spin coupled to the helical edge states of the Kane-Mele model
• Experimental realization of Majorana hinge and corner modes in intrinsic organic topological superconductor without magnetic field at room temperature
• Exotic domain walls in Bose-Einstein condensates with double-well dispersion
• Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator
• Control of Plasmons in Topological Insulators via Local Perturbations
• Homotopy invariant in time-reversal and twofold rotation symmetric systems
• Dynamic melting and condensation of topological dislocation modes
• Classification of unitary operators by local generatability
• Trapping of Spin-0 fields on tube-like topological defects
• Floquet-Anderson localization in the Thouless pump and how to avoid it
• PT-symmetric Non-Hermitian Hopf Metal
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Triangular lattice Majorana-Hubbard model: Mean field theory and DMRG on a width-4 torus
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Majorana edge states and topological properties in 1D/2D Rashba semiconductor proximity coupled to iron-based superconductor
• Modulating Hamiltonian Approach to Quantum Many-Body Systems and Crystalline Topological Phases Protected by Generalized Magnetic Translations
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Genuine topological Anderson insulator from impurity induced chirality reversal
• Dispersive nodal fermions along grain boundaries in Floquet topological crystals
• Topological and fractal defect states in non-Hermitian lattices
• Topological zero modes and bounded modes at smooth domain walls: Exact solutions and dualities
• Nodal lines and boundary modes in topological Dirac semimetals with magnetism
• Angular momentum of vortex-core Majorana zero modes
• Neutrino zeromodes on electroweak strings in light of topological insulators
• C*-framework for higher-order bulk-boundary correspondences
• Topological Description of the Solidification of Undercooled Fluids and the Temperature Dependence of the Thermal Conductivity of Crystalline and Glassy Solids Above Approximately 50 K
• Zero modes of velocity field and topological invariant in quantum torus
• Solidification of Icosahedral Quasicrystals: Viewpoint Based on a Quaternion Orientational Order Parameter and the Formation of the E8 Lattice
• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism
• Fragile dislocation modes in obstructed atomic topological phases
• Scalar field models driven by Dirac-Born-Infeld dynamics and their relatives
• Engineering Majorana Kramers Pairs In Synthetic High Spin Chern Insulators
• Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology
• Gauge fields induced by curved spacetime
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Majorana Flat Bands in the Vortex Line of Superconducting Weyl Semimetals
• Intrinsic non-Hermitian topological phases
• Surface states around a vortex in topological superconductors: Intersection of a surface and a vortex
• Coherence Effects of Caroli-de Gennes-Matricon Modes in Nodal Topological Superconductors
• Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping
• Topological invariant of velocity field in quantum systems
• $2+1$ dimensional Floquet systems and lattice fermions: Exact bulk spectral equivalence
• Inversion-symmetric Electron Gases as New Platforms for Topological Planar Josephson Junctions
• Persistence of phase boundaries between a topological and trivial Z2 insulator
• Topological Phase Transitions and Edge-State Transfer in Time-Multiplexed Quantum Walks
• Changes of Kondo effect in the junction with DIII-class topological and $s$-wave superconductors
• Kinklike structures in an arcsin real scalar dynamics
• Emergent One-Dimensional Helical Channel in Higher-Order Topological Insulators with Step Edges
• Topological superconductivity and fractional Josephson effect in quasi-one dimensional wires on a plane
• Dynamical Symmetry Indicators for Floquet Crystals
• Theory of classical electrodynamics with topologically quantized singularities as electric charges
• Discrete global symmetries and dynamics of emergent fermions
• Theory of Berry Singularity Markers: Diagnosing Topological Phase Transitions via Lock-In Tomography
• Topological phase states of the SU(3) QCD
• Topological Dislocation Response in Elementary Semiconductors
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries
• Semiconductor Meta-Graphene and Valleytronics
• Orbital Frontiers: Harnessing Higher Modes in Photonic Simulators
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Line defects in infinite networks of resistors
• Classification of topological insulators and superconductors with multiple order-two point group symmetries
• Topological quantum electrodynamics in synthetic non-Abelian gauge fields
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
• Topologically nontrivial multicritical points
• Buried Dirac points in quantum spin Hall insulators: Implications for Majorana Kramers pair-based quantum computing
• Single $\pi$-flux hosting topological defect modes in bilayer acoustic metamaterials
• Topological Tenfold Classification and the Entanglement of Two Qubits
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Dissipative quantum mechanics and Kondo-like impurities on noncommutative two-tori
• Zero energy modes with Gaussian, exponential, or polynomial decay: Exact solutions in hermitian and nonhermitian regimes
• Topological properties of domain walls in antiferromagnetic topological insulators
• Symmetry-protected topological wire in a topological vacuum
• Interacting Majorana fermions in strained nodal superconductors
• Josephson and persistent currents in a quantum ring between topological superconductors
• Topological defects in a double-mirror quadrupole insulator displace diverging charge
• Topology with broken parity-time symmetry
• Fractional spin Josephson effect in topological spin superconductors
• A $C^{\ast }$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals