Structure and Topology of Band Structures in the 1651 Magnetic Space Groups

Abstract

The properties of electrons in magnetically ordered crystals are of interest both from the viewpoint of realizing novel topological phases, such as magnetic Weyl semimetals, and from the applications perspective of creating energy-efficient memories. A systematic study of symmetry and topology in magnetic materials has been challenging given that there are 1651 magnetic space groups (MSGs). Here, by using an efficient representation of allowed band structures, we obtain a systematic description of several basic properties of free electrons in all MSGs in three dimensions as well as in the 528 magnetic layer groups relevant to two dimensional magnetic materials. We compute constraints on electron fillings and band connectivity compatible with insulating behavior. Also, by contrasting with atomic insulators, we identify band topology entailed by the symmetry transformation of bands, as determined by the MSG alone. We give an application of our results to identifying topological semimetals arising in periodic arrangements of hedgehog-like magnetic textures.

(9 + 34) pages; 3 figures; (2+19) tables; v2: close to published version

References in corpus (21)

• Topological Insulators with Inversion Symmetry
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Antiferromagnetic topological insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn
• Fragile Topology and Wannier Obstructions
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• The insulator/Chern-insulator transition in the Haldane model
• A hidden constant in the anomalous Hall effect of a high-purity magnet MnSi
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Rotation Anomaly and Topological Crystalline Insulators
• Graph Theory Data for Topological Quantum Chemistry
• Chirality induced anomalous-Hall effect in helical spin crystals
• Compactly-supported Wannier functions and algebraic $K$-theory
• Antiferromagnetic Dirac Semimetals in Two Dimensions
• The Lieb-Schultz-Mattis-type filling constraints in the 1651 magnetic space groups
• Space group symmetries and low lying excitations of many-body systems at integer fillings

Cited by in corpus (178)

• Symmetry and Topology in Non-Hermitian Physics
• Altermagnetism: spin-momentum locked phase protected by non-relativistic symmetries
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Progress and prospects in magnetic topological materials
• High-throughput calculations of magnetic topological materials
• Fragile Topology and Wannier Obstructions
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Magnetic Topological Quantum Chemistry
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• Electronic Transport and quantum oscillation of Topological Semimetals
• Topological Semimetals from first-principles
• Spin-group symmetry in magnetic materials with negligible spin-orbit coupling
• Chemical Principles of Topological Semimetals
• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Efficient Topological Materials Discovery Using Symmetry Indicators
• Topological Materials Discovery from Crystal Symmetry
• Realization of an intrinsic, ferromagnetic topological state in MnBi8Te13
• Enumeration and representation theory of spin space groups
• Tunable Weyl and Dirac states in the nonsymmorphic compound $\mathbf{CeSbTe}$
• Topological phases without crystalline counterparts
• Enumeration of spin-space groups: Towards a complete description of symmetries of magnetic orders
• First Principles Calculations for Topological Quantum Materials
• Dirac semimetal in type IV magnetic space group
• Quantum transport evidence of Weyl fermions in an epitaxial ferromagnetic oxide
• Band Representations and Topological Quantum Chemistry
• From colossal to zero: Controlling the Anomalous Hall Effect in Magnetic Heusler Compounds via Berry Curvature Design
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Topological spin excitations observed in a three-dimensional antiferromagnet
• Intrinsic axion insulating behavior in antiferromagnetic MnBi${}_6$Te${}_{10}$
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Topological correspondence between magnetic space group representations
• Magnetic crystalline-symmetry-protected axion electrodynamics and field-tunable unpinned Dirac cones in EuIn2As2
• 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
• Unified understanding of symmetry indicators for all internal symmetry classes
• Half-Magnetic Topological Insulator
• Observation of spin-momentum locked surface states in amorphous Bi${}_2$Se${}_3$
• Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons
• Phase diagram of disordered higher-order topological insulator: A machine learning study
• Spin-Space Groups and Magnon Band Topology
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Multifold nodal points in magnetic materials
• Bicircular light tuning of magnetic symmetry and topology in Dirac semimetal Cd${}_3$As${}_2$
• Spectral signatures of the surface anomalous Hall effect in magnetic axion insulators
• Symmetry indicators of band topology
• High-throughput search for magnetic and topological order in transition metal oxides
• Catalogue of topological phonon materials
• Altermagnetism and magnetic groups with pseudoscalar electron spin
• ${\mathbb{Z}}_2$ Topological Invariant for Magnon Spin Hall Systems
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• Topological Materials Discovery By Large-order symmetry indicators
• Three-dimensional superconductors with hybrid higher order topology
• Encyclopedia of emergent particles in type-IV magnetic space groups
• Temperature Dependent Electronic Structure in a Higher Order Topological Insulator Candidate EuIn${}_2$As${}_2$
• Topological classification and diagnosis in magnetically ordered electronic materials
• Non-Hermiticity and topological invariants of magnon Bogoliubov-de Gennes systems
• Atiyah-Hirzebruch Spectral Sequence in Band Topology: General Formalism and Topological Invariants for 230 Space Groups
• Multiple magnetic topological phases in bulk van der Waals crystal MnSb4Te7
• Higher order topological superconductors as generators of quantum codes
• Conversion rules for Weyl points and nodal lines in topological media
• Symmetry indicators for topological superconductors
• A systematic study of stacked square nets: from Dirac fermions to material realizations
• Complete classification of band nodal structures
• Qsymm: Algorithmic symmetry finding and symmetric Hamiltonian generation
• Subdimensional topologies, indicators and higher order phases
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Magnetic and electronic properties of a topological nodal line semimetal candidate: HoSbTe
• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Non-local topological electromagnetic phases of matter
• General construction of flat bands with and without band crossings based on wave function singularity
• Topological electronic structure in the antiferromagnet HoSbTe
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Fragile topologically flat band in the checkerboard antiferromagnetic monolayer FeSe
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Axion coupling in the hybrid Wannier representation
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• Machine learning spectral indicators of topology
• Delocalization Transition of Disordered Axion Insulator
• What's knot to like? Observation of a linked loop quantum state
• Faithful derivation of symmetry indicators: A case study for topological superconductors with time-reversal and inversion symmetries
• Piezoelectricity and Topological Quantum Phase Transitions in Two-Dimensional Spin-Orbit Coupled Crystals with Time-Reversal Symmetry
• Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling
• Consecutive topological phase transitions and colossal magnetoresistance in a magnetic topological semimetal
• Doubled Quantum Spin Hall Effect with High-Spin Chern Number in $\alpha$-Antimonene and $\alpha$-Bismuthene
• Topological continuum charges of acoustic phonons in 2D
• Location and topology of the fundamental gap in photonic crystals
• Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
• Intrinsic Magnetic Topological Materials
• Rare-earth monopnoctides -- family of antiferromagnets hosting magnetic Fermi arcs
• Symmetry-based approach to nodal structures: Unification of compatibility relations and gapless point classifications
• Calculated magnetic exchange interactions in Dirac magnon material Cu3TeO6
• No-go theorem for topological insulators and sure-fire recipe for Chern insulators
• Chiral Dirac-like fermion in spin-orbit-free antiferromagnetic semimetals
• Symmetry-protected Nodal Points and Nodal Lines in Magnetic Materials
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Non-Compact Atomic Insulators
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Ferromagnetic nodal-line metal in monolayer {\em h}-InC
• Identifying, and constructing, complex magnon band topology
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• The Bulk-Hinge Correspondence and Three-Dimensional Quantum Anomalous Hall Effect in Second Order Topological Insulators
• MSGCorep: A package for corepresentations of magnetic space groups
• Coexistence of Weyl semimetal and Weyl nodal loop semimetal phases in a collinear antiferromagnet
• Large shift current, $\pi$ Zak phase and unconventional nature in Se and Te
• Higher-order Topological Phases of Magnons in van der Waals Honeycomb Ferromagnets
• Discovering two-dimensional magnetic topological insulators by machine learning
• Structural disorder-driven topological phase transition in noncentrosymmetric BiTeI
• Investigating global and topological order of states by local measurement and classical communication: Study on SPT phase diagrams by quantum energy teleportation
• Variants of the symmetry-based indicator
• Novel topological insulators from crystalline symmetries
• Unsupervised learning of topological phase diagram using topological data analysis
• From Atomic Semimetal to Topological Nontrivial Insulator
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Colloquium: Synthetic quantum matter in non-standard geometries
• Efficient Design of Helical Higher-Order Topological Insulators in 3D Elastic Medium
• Abundant surface-semimetal phases in three-dimensional obstructed atomic insulators
• Topology in time-reversal symmetric crystals
• Highly Tunable Band Inversion in AB2X4 (A=Ge, Sn, Pb; B=As, Sb, Bi; X=Se, Te) Compounds
• Antiferromagnetic topological insulator with selectively gapped Dirac cones
• Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice
• Orbital shift-induced boundary obstructed topological materials with a large energy gap
• Hund nodal line semimetals: The case of twisted magnetic phase in the double-exchange model
• Magnetic band representations, Fu-Kane-like symmetry indicators and magnetic topological materials
• Antisymmetry: Fundamentals and Applications
• Topological $Z_2$ invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group
• Projected spin texture as a bulk indicator of fragile topology
• Intrinsic ferromagnetic axion states and a single pair of Weyl fermions in the stable-state Mn\emph{X}${}_2$\emph{B}${}_2$\emph{T}${}_6$-family materials
• Magnetic hourglass fermions: from exhaustive symmetry conditions to high-throughput materials predictions
• Unconventional Surface State Pairs in a High-Symmetry Lattice with Anti-ferromagnetic Band-folding
• Topological Magnetoelectric Effect: Nonlinear Time-Reversal-Symmetric Response, Witten Effect, and Half-Integer Quantum Hall Effect
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
• Higher-order topological superconductivity in a topological metal 1T${}^{\prime }$-MoTe${}_2$
• Long-Time Magnetic Relaxation in Antiferromagnetic Topological Material EuCd${}_2$As${}_2$
• Topological phase diagrams of in-plane field polarized Kitaev magnets
• Intrinsic ferromagnetic and antiferromagnetic axion insulators in van der Waals materials Mn\emph{X}${}_2$\emph{B}${}_2$\emph{T}${}_6$ family
• Topology in abundance
• Low-energy Properties of Electrons and Holes in CuFeS${}_2$
• Multi-type Dirac fermions protected by orthogonal glide symmetries in a noncentrosymmetric system
• Topological gapless points in superconductors: From the viewpoint of symmetry
• Classification of symmetry-enriched topological quantum spin liquids
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• The topological invariants of rotationally symmetric crystals
• Topological metals constructed by sliding quantum wire arrays
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• A topological classification of molecules and chemical reactions with a perplectic structure
• XFe4Ge2 (X = Y, Lu) and Mn3Pt: Filling-enforced magnetic topological metals
• A Hamiltonian Approach for Obtaining Irreducible Projective Representations and the $k\cdot p$ Perturbation for Anti-unitary Symmetry Groups
• Intrinsic antiferromagnetic topological insulator and axion state in V2WS4
• Flavors of Magnetic Noise in Quantum Materials
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Nonsymmorphic bosonization in one-dimensional generalized Kitaev spin-1/2 models
• Topological phases of amorphous matter
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Topological Descendants of Multicritical EuTl2
• The Future of the Correlated Electron Problem
• General corner charge formulas in various tetrahedral and cubic space groups
• Visualising the connection between edge states and the mobility edge in adiabatic and non-adiabatic topological charge transport
• Topological Signatures in Nodal Semimetals through Neutron Scattering
• Hall effect of ferro/antiferromagnetic wallpaper fermions
• Nonsymmorphic spin-space cubic groups and SU(2)${}_1$ conformal invariance in one-dimensional spin-1/2 models
• Topological States in Chevrel Phase Materials from First-principle Calculations
• Theory of fractional corner charges in cylindrical crystal shapes
• Topological Anderson insulators by latent symmetry
• Field-driven band asymmetry and non-reciprocal transport in a helimagnet
• Anomalous Hall effect in the antiferromagnetic Weyl semimetal SmAlSi
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Topological band insulators without translational symmetry
• Tunable topological phase in 2D ScV${}_6$Sn${}_6$ kagome material
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Hidden wallpaper fermion and third-order topological insulator
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges
• Topological Charge Quadrupole Protected by Spin-Orbit U(1) Quasi-Symmetry in Antiferromagnet NdBiPt
• Optical Response from Charge-Density Waves in Weyl Semimetals
• Non-self-averaging topological Anderson insulator
• Detection of 2D SPT Order with Partial Symmetries