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.

153 pages, 21 figures

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Cited by in corpus (24)

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• Chiral Dirac-like fermion in spin-orbit-free antiferromagnetic semimetals
• Large shift current, $\pi$ Zak phase and unconventional nature in Se and Te
• From Atomic Semimetal to Topological Nontrivial Insulator
• Abundant surface-semimetal phases in three-dimensional obstructed atomic insulators
• Magnetic band representations, Fu-Kane-like symmetry indicators and magnetic topological materials
• Origin of the exotic electronic states in antiferromagnetic NdSb
• Constructions and Applications of Irreducible Representations of Spin-Space Groups
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
• Axion insulators protected by C2T and their K-theory invariants and material realization
• The evolution of Weyl nodes in Ni doped thallium niobate pyrochlore Tl${}_{2-x}$Ni${}_x$Nb${}_2$O${}_7$
• Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries
• 5d orbital Induced Room Temperature Quantum Anomalous Hall Effect in TbCl
• Altermagnetic Weyl node-network semimetals protected by spin symmetry
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Spectroscopic signatures of magnetization-induced band renormalization and strong spin-charge-lattice coupling in EuZn${}_2$As${}_2$
• Intrinsic (Axion) Statistical Topological Insulator
• High-throughput search for topological magnon materials
• Topological Charge Quadrupole Protected by Spin-Orbit U(1) Quasi-Symmetry in Antiferromagnet NdBiPt