Topological classification and diagnosis in magnetically ordered electronic materials

Abstract

We show that compositions of time-reversal and spatial symmetries, also known as the magnetic-space-group symmetries, protect topological invariants as well as surface states that are distinct from those of all preceding topological states. We obtain, by explicit and exhaustive construction, the topological classification of electronic band insulators that are magnetically ordered for each one of the 1421 magnetic space groups in three dimensions. We have also computed the symmetry-based indicators for each nontrivial class, and, by doing so, establish the complete mapping from symmetry representations to topological invariants.

arXiv comment153 pages, 21 figures

References in corpus (93)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Unpaired Majorana fermions in quantum wires
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Insulators in Three Dimensions
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological invariants of time-reversal-invariant band structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• Topological Crystalline Insulators in the SnTe Material Class
• Giant anomalous Hall effect in a ferromagnetic Kagome-lattice semimetal
• Prediction and observation of the first antiferromagnetic topological insulator
• The (High Quality) Topological Materials In The World
• Intrinsic magnetic topological insulators in van der Waals layered MnBi${}_2$Te${}_4$-family materials
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Anomalous Hall Effect and Magnetic Monopoles in Momentum-Space
• Catalogue of Topological Electronic Materials
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Topological axion states in magnetic insulator MnBi${}_2$Te${}_4$ with the quantized magnetoelectric effect
• Magnetic Weyl Semimetal Phase in a Kagome Crystal
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Experimental realization of an intrinsic magnetic topological insulator
• Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co3Sn2S2
• Antiferromagnetic topological insulators
• Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions
• Topological classification of crystalline insulators through band structure combinatorics
• Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet
• Inversion Symmetric Topological Insulators
• Dynamical Axion Field in Topological Magnetic Insulators
• Topology of crystalline insulators and superconductors
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• High-throughput calculations of magnetic topological materials
• Hourglass Fermions
• Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn
• Time-Reversal-Breaking Weyl Fermions in Magnetic Heusler Alloys
• Irvsp: to obtain irreducible representations of electronic states in the VASP
• Quantitative mappings between symmetry and topology in solids
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Dirac Fermions in Antiferromagnetic Semimetal
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Magnetic Topological Quantum Chemistry
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Large magnetic gap at the Dirac point in a Mn-induced Bi${}_2$Te${}_3$ heterostructure
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Topological phases protected by point group symmetry
• Building crystalline topological phases from lower-dimensional states
• Room-temperature magnetic topological semimetal state in half-metallic Heusler Co${}_2$TiX (X=Si, Ge, or Sn)
• Gauging spatial symmetries and the classification of topological crystalline phases
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topology of nonsymmorphic crystalline insulators and superconductors
• Topological non-symmorphic crystalline insulators
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Rotation Anomaly and Topological Crystalline Insulators
• Symmetry Enforced Chiral Hinge States and Surface Quantum Anomalous Hall Effect in Magnetic Axion Insulator ${\text{Bi}}_{2-x}{\text{Sm}}_x{\text{Se}}_3$
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Dirac semimetal in type IV magnetic space group
• Theory of interacting topological crystalline insulators
• Topological Insulators with Commensurate Antiferromagnetism
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• Diagnosis for topological semimetals in the absence of spin-orbital coupling
• The study of magnetic topological semimetals by first principles calculations
• Topological correspondence between magnetic space group representations
• Topological states from topological crystals
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Unified understanding of symmetry indicators for all internal symmetry classes
• Crystalline topological phases as defect networks
• Topological nodal-line semimetals in ferromagnetic rare-earth-metal monohalides
• Classification and construction of higher-order symmetry protected topological phases of interacting bosons
• Topological magnetic crystalline insulators and co-representation theory
• Real-space recipes for general topological crystalline states
• Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
• Topological semimetal in honeycomb lattice LnSI
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Axion coupling in the hybrid Wannier representation
• The classification of surface states of topological insulators and superconductors with magnetic point group symmetry
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Hinge Spin Polarization in Magnetic Topological Insulators Revealed by Resistance Switch
• Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice

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