Magnetic band representations, Fu-Kane-like symmetry indicators and magnetic topological materials

Abstract

To realize novel topological phases and to pursue potential applications in low-energy consumption spintronics, the study of magnetic topological materials is of great interest. Starting from the theory of nonmagnetic topological quantum chemistry [Bradlyn et al., Nature 547, 298 (2017)], we have obtained irreducible (co)representations and compatibility relations (CRs) in momentum space, and we constructed a complete list of magnetic band (co)representations (MBRs) in real space for other MSGs with anti-unitary symmetries (i.e. type-III and type-IV MSGs). The results are consistent with the magnetic topological quantum chemistry [Elcoro et al., Nat. Comm. 12, 5965 (2021)]. Using the CRs and MBRs, we reproduce the symmetry-based classifications for MSGs, and we obtain a set of Fu-Kane-like formulas of symmetry indicators (SIs) in both spinless (bosonic) and spinful (fermionic) systems, which are implemented in an automatic code - TopMat - to diagnose topological magnetic materials. The magnetic topological materials, whose occupied states can not be decomposed into a sum of MBRs, are consistent with nonzero SIs. Lastly, using our online code, we have performed spin-polarized calculations for magnetic compounds in the materials database and find many magnetic topological candidates.

arXiv comment6 pages, 3128 pages for the Appendices

References in corpus (41)

• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Insulators in Three Dimensions
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Topological Crystalline Insulators
• Three Dimensional Dirac Semimetal and Quantum Transports in Cd3As2
• 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
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• The (High Quality) Topological Materials In The World
• Observation of Weyl nodes in TaAs
• Catalogue of Topological Electronic Materials
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Inversion Symmetric Topological Insulators
• High-throughput calculations of magnetic topological materials
• Hourglass Fermions
• 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
• 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
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSb
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Graph Theory Data for Topological Quantum Chemistry
• Topological correspondence between magnetic space group representations
• Magnetic semimetals and quantized anomalous Hall effect in EuB6
• Unconventional Materials: the mismatch between electronic charge centers and atomic positions
• Topological magnetic crystalline insulators and co-representation theory
• Topological classification and diagnosis in magnetically ordered electronic materials
• Subdimensional topologies, indicators and higher order phases
• Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
• High-throughput screening for Weyl Semimetals with S${}_4$ Symmetry

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