The space group classification of topological band insulators

Abstract

Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice symmetries in the physics of these topological states remained elusive. Here we provide the classification of TBIs protected not only by time-reversal, but also by crystalline symmetries. We find three broad classes of topological states: (a) Gamma-states robust against general time-reversal invariant perturbations; (b) Translationally-active states protected from elastic scattering, but susceptible to topological crystalline disorder; (c) Valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route for the systematic search for new types of TBIs.

Accepted in Nature Physics

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• Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
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• MPd5 kagome superconductors studied by density functional calculations
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• Enhancing the Hyperpolarizability of Crystals with Quantum Geometry
• A New Magnetic Topological Quantum Material Candidate by Design
• Non-trivial topological valence bands of common diamond and zinc-blende semiconductors
• Topological Anderson insulators by latent symmetry
• The destiny of obstructed atomic insulator under correlation
• Selective branching, quenching, and converting of topological modes
• Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation
• Hybrid symmetry class topological insulators
• Mapping rules from nodal line semimetal to topological crystalline insulator in face centered cubic lattice
• Fragile topology in nodal-line semimetal superconductors
• Topologically-enhanced exciton transport
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• Hedgehog spin texture and competing orders associated with strains on the surface of a topological crystalline insulator
• Dynamic melting and condensation of topological dislocation modes
• Band structure picture for topology in strongly correlated systems with the ghost Gutzwiller ansatz
• Interacting Virtual Topological Phases in Defect-Rich 2D Materials
• Arboreal Obstructed Atomic Insulating and Metallic Phases of Fermions
• Adiabatic pumping and transport in the Sierpinski-Hofstadter model
• Interaction-driven phase transition in one dimensional mirror-symmetry protected topological insulator
• Topological Aspects of Antiferromagnets
• Stability of the X-Y-phase of the two-dimensional C4 point group insulator
• Fermiology and transport properties of the proposed topological crystalline insulator SrAg4Sb2
• Role of effective mass anisotropy in realizing a hybrid nodal-line fermion state
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Hopf Semimetals
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Topological Charge Quadrupole Protected by Spin-Orbit U(1) Quasi-Symmetry in Antiferromagnet NdBiPt
• Crystalline finite-size topology
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• 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
• Fragile dislocation modes in obstructed atomic topological phases
• 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
• Predicted versatile topological nodal magnons in Tb-based icosahedral quasicrystal 1/1 approximants
• Inter-species topological phases via a dynamical gauge field
• Obstructed Atomic Insulators and Superfluids of Fermions Coupled to ${\mathbb{Z}}_2$ Gauge Fields
• Preserving Topology while Breaking Chirality: From Chiral Orthogonal to Anti-symmetric Hermitian Ensemble
• Emergence of a new symmetry class for Bogoliubov-de Gennes (BdG) Hamiltonians: Expanding ten-fold symmetry classes
• Universal Broadening of Zero Modes: A General Framework and Identification
• Topological property of graphene with triangular array of nanoholes
• Effect of superconductivity by Nb and V substitution in kagome CaPd5
• Proposal for realizing and probing topological crystalline insulators in optical lattices
• Signature of topological crystalline insulating behavior in new B2X2Zn (X=Ir, Rh, Co) compound from first-principles Computation
• Vortical Quantum Memory
• Physical Pictures for Quasisymmetry in Crystals
• Robust zero-energy states in two-dimensional Su-Schrieffer-Heeger topological insulators
• Non-unique connection between bulk topological invariants and surface physics
• Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries
• Orbital magnetization reveals multiband topology
• Intrinsic one-dimensional conducting channels in the Kondo insulator SmB6
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases