Symmetry-based Indicators of Band Topology in the 230 Space Groups

Abstract

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials.

9+21 pages; (2+1) figures, (4+20) tables; v2: references added; title changed; results for quasi-2D and 1D systems added

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• Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
• Andreev reflection in Euler materials
• Constructions and Applications of Irreducible Representations of Spin-Space Groups
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• Bulk Pumping in 2D Topological Phases
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• Higher-order topological insulators in a crisscross antiferromagnetic model
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• Multiple superconducting phases driven by pressure in the topological insulator GeSb4Te7
• The topological invariants of rotationally symmetric crystals
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• Anomalous Crystal Shapes of Topological Crystalline Insulators
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• Multi-type Dirac fermions protected by orthogonal glide symmetries in a noncentrosymmetric system
• Pfaffian invariant identifies magnetic obstructed atomic insulators
• Nonlinear breathers with crystalline symmetries
• Diagnosis of topological nodal lines with nontrivial monopole charge in the presence of rotation symmetries
• Topology in abundance
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
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• Band alignment effect in the topological photonic alloy
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• Turning Copper Metal into Weyl Semimetal
• Topological metals constructed by sliding quantum wire arrays
• STM observation of the hinge-states of bismuth nanocrystals
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• $T_3$Pb${}_{2}C{h}_2$ ($T$=Pd,Pt and $Ch$=S,Se) with transition metal kagome net: Dynamical properties, phonon nodal line, phonon surface states, and chiral phonons
• Fractional corner charges in threefold-symmetric two-dimensional materials with fragile topology
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• Optical signatures of Euler superconductors
• Altermagnetic Weyl node-network semimetals protected by spin symmetry
• Discovery of topological metamaterials by symmetry relaxation and smooth topological indicators
• Chern dartboard insulator: sub-Brillouin zone topology and skyrmion multipoles
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• Second Euler number in four dimensional synthetic matter
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
• Nonsymmorphic bosonization in one-dimensional generalized Kitaev spin-1/2 models
• Characterization of higher-order topological superconductors using Bott indices
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Topological end states in a one-dimensional spatially modulated interaction spinless fermion model
• $Z_2$ Dirac points with topologically protected multihelicoid surface states
• Intrinsic antiferromagnetic topological insulator and axion state in V2WS4
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• MPd5 kagome superconductors studied by density functional calculations
• Two-dimensional orbital-obstructed insulators with higher-order band topology
• Flat bands in condensed-matter systems -- perspective for magnetism and superconductivity
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Pumping with Symmetry
• Topological Signatures in Nodal Semimetals through Neutron Scattering
• An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped Invariants related to corner states
• Recipe for higher-order topology on the triangular lattice
• Correlated Zak insulator in organic antiferromagnets
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Topological Descendants of Multicritical EuTl2
• Quantized thermal and spin transports of dirty planar topological superconductors
• Topology of SmB6 revisited by means of topological quantum chemistry
• General corner charge formulas in various tetrahedral and cubic space groups
• Ideal Spin-Orbit-Free Dirac Semimetal and Diverse Topological Transitions in Pr${}_8$CoGa${}_3$ Family
• Polarization textures in crystal supercells with topological bands
• Topological insulators on fractal lattices: A general principle of construction
• Visualising the connection between edge states and the mobility edge in adiabatic and non-adiabatic topological charge transport
• Hong-Ou-Mandel Interference in a temporal-average-inversion-symmetric chain
• Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
• Quantum geometric bounds in spinful systems with trivial band topology
• Enhancing the Hyperpolarizability of Crystals with Quantum Geometry
• Projective Representations, Bogomolov Multiplier, and Their Applications in Physics
• Exciton Berryology
• Theoretical analysis of glide-Z_2 magnetic topological photonic crystals
• Topological Anderson insulators by latent symmetry
• Hermitian and non-Hermitian topology in active matter
• Topologically-enhanced exciton transport
• Selective branching, quenching, and converting of topological modes
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• Universality of Abelian and non-Abelian Wannier functions in one dimension
• Simple realization of a fragile topological lattice with quasi flat-bands in a microcavity array
• Theory of fractional corner charges in cylindrical crystal shapes
• Nonsymmorphic spin-space cubic groups and SU(2)${}_1$ conformal invariance in one-dimensional spin-1/2 models
• Intrinsic (Axion) Statistical Topological Insulator
• Fragile topology in nodal-line semimetal superconductors
• Topological Micro-Electro-Mechanical Systems
• Topological Dynamics and Correspondences in Composite Exceptional Rings
• $d$-Wave Polarization-Spin Locking in Two-Dimensional Altermagnets
• Magneto-optical Conductance of Kane Fermion Gas in Low Frequencies
• Transversality-Enforced Tight-Binding Models for 3D Photonic Crystals aided by Topological Quantum Chemistry
• Mapping rules from nodal line semimetal to topological crystalline insulator in face centered cubic lattice
• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
• Homotopy invariant in time-reversal and twofold rotation symmetric systems
• Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The ${\lambda }_N$-Jellium model
• IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures
• The destiny of obstructed atomic insulator under correlation
• Topological insulators and geometry of vector bundles
• Atomically thin obstructed atomic insulators with robust edge modes and quantized spin Hall effect
• Topological Spectral Bands with Frieze Groups
• Gapless Topological Peierls-like instabilities in more than one dimension
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Local symmetry groups for arbitrary wavevectors
• Absence of superconductivity in topological metal ScInAu${}_2$
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Stacked tree construction for free-fermion projected entangled pair states
• High-throughput search for topological magnon materials
• Isotropic 3D topological phases with broken time reversal symmetry
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Network model for magnetic higher-order topological phases
• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Topological invariant and domain connectivity in moiré materials
• Spacetime symmetry indicators for two-dimensional Floquet topological insulators
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Anomalous wave-packet transport on boundaries of Floquet topological systems
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Disclinations, dislocations, and emanant flux at Dirac criticality
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• Frustration-free free fermions
• Topological band insulators without translational symmetry
• Laser-induced topological phases in monolayer amorphous carbon
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges
• Topological constraints on the electronic band structure of hexagonal lattice in a magnetic field
• Majorana Zero Modes and Topological Nature in Bi2Ta3S6-family Superconductors
• Predicting Many Crystal Properties via an Adaptive Transformer-based Framework
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Higher Chern bands in helical homotrilayer transition metal dichalcogenides
• Efficient prediction of topological superlattice bands with spin-orbit coupling
• Nodal-line semimetal HMTSF-TCNQ: Anomalous orbital diamagnetism and charge density wave
• Three-dimensional spinless Euler insulators with rotational symmetry
• The mixing-spacetime symmetry in the Floquet-Bloch band theory
• Orbital magnetization reveals multiband topology
• Towards a Topological Quantum Chemistry description of correlated systems: the case of the Hubbard diamond chain
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Periodic Behavior of Topology in Graphene with Nanohole Array
• Topological property of graphene with triangular array of nanoholes
• Non-self-averaging topological Anderson insulator
• Quantized Spin Hall Effect in Three-Dimensional Nodal-Ring Semimetal: Geometric Scaling and Symmetry-Engineered Spin Response
• Effect of superconductivity by Nb and V substitution in kagome CaPd5
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Dynamical Symmetry Indicators for Floquet Crystals
• Detection of 2D SPT Order with Partial Symmetries
• Higher-order topological insulator in cubic semiconductor quantum wells
• Symmetry-Based Real-Space Framework for Realizing Flat Bands and Unveiling Nodal-Line Touchings
• Systematic study for two-dimensional $Z_2$ topological phase transitions at high-symmetry points in all layer groups
• ToMSGKpoint: A user-friendly package for computing symmetry transformation properties of electronic eigenstates of nonmagnetic and magnetic crystalline materials
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Topological Invariants of a Filling-Enforced Quantum Band Insulator
• When Wannier centers jump: Critical points between atomic insulating phases
• Orbital Frontiers: Harnessing Higher Modes in Photonic Simulators
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases