Topological correspondence between magnetic space group representations

Abstract

The past years have seen rapid progress in the classification of topological materials. These diagnostical methods are increasingly getting explored in the pertinent context of magnetic structures. We report on a general class of electronic configurations within a set of anti-ferromagnetic-compatible space groups that are necessarily topological. Interestingly, we find a systematic correspondence between these anti-ferromagnetic phases to necessarily nontrivial topological ferro/ferrimagnetic counterparts that are readily obtained through physically motivated perturbations. Addressing the exhaustive list of magnetic space groups in which this mechanism occurs, we also verify its presence on planes in 3D systems that were deemed trivial in existing classification schemes. This leads to the formulation of the concept of subdimensional topologies, featuring non-triviality within part of the system that coexists with stable Weyl points away from these planes, thereby uncovering novel topological materials in the full 3D sense that have readily observable features in their bulk and surface spectrum.

arXiv comment16+8 pages, 11+2 figures;new version comprises extensive updates upon combining previous manuscript with a follow-up study

References in corpus (84)

• Topological Insulators
• Topological insulators and superconductors
• Maximally-localized generalized Wannier functions for composite energy bands
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Crystalline Insulators
• Topological quantum chemistry
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• Prediction and observation of the first antiferromagnetic topological insulator
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Topological nodal line semimetals with and without spin-orbital coupling
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Non-Hermitian Boundary Modes
• Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Antiferromagnetic topological insulators
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Inversion Symmetric Topological Insulators
• Nodal-chain metals
• Topology of crystalline insulators and superconductors
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• All "Magic Angles" Are "Stable" Topological
• Wannier representation of Z_2 topological insulators
• Topological quantum properties of chiral crystals
• Multiple types of topological fermions in transition metal silicides
• Hourglass Fermions
• Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
• Large Fermi Arcs in Unconventional Weyl Semimetal RhSi
• Fragile Topology and Wannier Obstructions
• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• A method for atomistic spin dynamics simulations: implementation and examples
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Magnetic Topological Quantum Chemistry
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Non-Abelian band topology in noninteracting metals
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology
• Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Wannier Center Sheets in Topological Insulators
• Non-Abelian reciprocal braiding of Weyl points and its manifestation in $\text{ZrTe}$
• Topological Quadrupolar Semimetals
• Topological Euler class as a dynamical observable in optical lattices
• Surfaces of Axion Insulators
• Topology of nonsymmorphic crystalline insulators and superconductors
• Unsupervised machine learning and band topology
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• Geometric approach to fragile topology beyond symmetry indicators
• Experimental characterization of fragile topology in an acoustic metamaterial
• Universal probes of two-dimensional topological insulators: Dislocation and pi-flux
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Topological Insulators from Group Cohomology
• Composite Weyl nodes stabilized by screw symmetry with and without time reversal
• Unified bulk-boundary correspondence for band insulators
• Hybrid Monte Carlo algorithm for the Double Exchange Model
• Topological Insulators with Commensurate Antiferromagnetism
• Twofold quadruple Weyl nodes in chiral cubic crystals
• Intrinsic axion insulating behavior in antiferromagnetic MnBi${}_6$Te${}_{10}$
• The Landau Level of Fragile Topology
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• The translational side of topological band insulators
• Berry-phase description of Topological Crystalline Insulators
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Filling-enforced Magnetic Dirac Semimetals in Two Dimensions
• The Axion Insulator as a Pump of Fragile Topology
• Fragile Phases As Affine Monoids: Classification and Material Examples
• Topological Bloch oscillations
• Hopf characterization of two-dimensional Floquet topological insulators
• Global band topology of simple and double Dirac-point (semi-)metals
• Topological magnetic crystalline insulators and co-representation theory
• Topological classification and diagnosis in magnetically ordered electronic materials
• Unconventional topological phase transition in two-dimensional systems with space-time inversion symmetry
• Wannier representation of Floquet topological states
• Subdimensional topologies, indicators and higher order phases
• Classification of crystalline insulators without symmetry indicators: atomic and fragile topological phases in twofold rotation symmetric systems
• Global topology of Weyl semimetals and Fermi arcs
• Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator
• Hund nodal line semimetals: The case of twisted magnetic phase in the double-exchange model
• Chiralities of nodal points along high symmetry lines with screw rotation symmetry
• Bulk topology of line-nodal structures protected by space group symmetries in class AI

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• Observation of non-Abelian topological semimetals and their phase transitions
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• Multi-gap topology and non-Abelian braiding of phonons from first principles
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• Optical manifestations and bounds of topological Euler class
• Machine learning spectral indicators of topology
• Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling
• Topological continuum charges of acoustic phonons in 2D
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Intrinsic Magnetic Topological Materials
• Rare-earth monopnoctides -- family of antiferromagnets hosting magnetic Fermi arcs
• Phase transitions of non-Abelian charged nodal links in a spring-mass system
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• Symmetry-protected Nodal Points and Nodal Lines in Magnetic Materials
• Chirality flip of Weyl nodes and its manifestation in strained MoTe${}_2$
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• From Atomic Semimetal to Topological Nontrivial Insulator
• Large-Gap Quantum Anomalous Hall Insulators in $A$Ti$X$ Class
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Abundant surface-semimetal phases in three-dimensional obstructed atomic insulators
• Group Theory on Quasisymmetry and Protected Near Degeneracy
• Magnetic band representations, Fu-Kane-like symmetry indicators and magnetic topological materials
• Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams
• Projected spin texture as a bulk indicator of fragile topology
• Origin of the exotic electronic states in antiferromagnetic NdSb
• Unconventional Surface State Pairs in a High-Symmetry Lattice with Anti-ferromagnetic Band-folding
• Dynamical Fragile Topology in Floquet Crystals
• Classification of Weyl points and nodal lines based on magnetic point groups for spin-$\frac{1}{2}$ quasiparticles
• Exact projected entangled pair ground states with topological Euler invariant
• Andreev reflection in Euler materials
• Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
• Constructions and Applications of Irreducible Representations of Spin-Space Groups
• Topotaxial Mutual-Exchange Growth of Magnetic Zintl Eu${}_3$In${}_2$As${}_4$ Nanowires with Axion Insulator Classification
• The evolution of Weyl nodes in Ni doped thallium niobate pyrochlore Tl${}_{2-x}$Ni${}_x$Nb${}_2$O${}_7$
• Fully linear band crossings at high symmetry points in layers: classification and role of spin-orbit coupling and time reversal
• Topological gapless points in superconductors: From the viewpoint of symmetry
• The topological invariants of rotationally symmetric crystals
• Optical signatures of Euler superconductors
• Altermagnetic Weyl node-network semimetals protected by spin symmetry
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
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• Tailoring Neel orders in Layered Topological Antiferromagnets
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• Selective branching, quenching, and converting of topological modes
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• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Mott transition and magnetism in a fragile topological insulator
• High-throughput search for topological magnon materials
• Non-Abelian interference of topological edge states
• Topological Charge Quadrupole Protected by Spin-Orbit U(1) Quasi-Symmetry in Antiferromagnet NdBiPt
• Weak ${\mathbb{Z}}_2$ Supertopology
• Emergence of Nodal-Knot Transitions by Disorder
• Hinge modes of three-dimensional Euler insulators
• Gapped spinful phases obtained via Gutzwiller projections of Euler states