Efficient Topological Materials Discovery Using Symmetry Indicators

Abstract

Although the richness of spatial symmetries has led to a rapidly expanding inventory of possible topological crystalline (TC) phases of electrons, physical realizations have been slow to materialize due to the practical difficulty to ascertaining band topology in realistic calculations. Here, we integrate the recently established theory of symmetry indicators of band topology into first-principle band-structure calculations, and test it on a databases of previously synthesized crystals. The combined algorithm is found to efficiently unearth topological materials and predict topological properties like protected surface states. On applying our algorithm to just 8 out of the 230 space groups, we already discover numerous materials candidates displaying a diversity of topological phenomena, which are simultaneously captured in a single sweep. The list includes recently proposed classes of TC insulators that had no previous materials realization as well as other topological phases, including: (i) a screw-protected 3D TC insulator, \b{eta}-MoTe2, with gapped surfaces except for 1D helical "hinge" states; (ii) a rotation-protected TC insulator BiBr with coexisting surface Dirac cones and hinge states; (iii) non-centrosymmetric Z2 topological insulators undetectable using the well-established parity criterion, AgXO (X=Na,K,Rb); (iv) a Dirac semimetal MgBi2O6; (v) a Dirac nodal-line semimetal AgF2; and (vi) a metal with three-fold degenerate band crossing near the Fermi energy, AuLiMgSn. Our work showcases how the recent theoretical insights on the fundamentals of band structures can aid in the practical goal of discovering new topological materials.

References in corpus (32)

• Topological Insulators
• Topological insulators and superconductors
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Insulators with Inversion Symmetry
• Topological Crystalline Insulators
• Quantum Spin Hall Effect and Topological Field Effect Transistor in Two-Dimensional Transition Metal Dichalcogenides
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Higher-Order Topology in Bismuth
• Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• The space group classification of topological band insulators
• Inversion Symmetric Topological Insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Spectroscopic evidence for type II Weyl semimetal state in MoTe2
• Observation of the Type-II Weyl Semimetal Phase in MoTe2
• Hourglass Fermions
• Fragile Topology and Wannier Obstructions
• Quantitative mappings between symmetry and topology in solids
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Fermi arcs and their topological character in the candidate type-II Weyl semimetal MoTe2
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• First-principles calculation of topological invariants Z2 within the FP-LAPW formalism
• Topological crystalline insulator states in the Ca${}_2$As family

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• Two-dimensional second-order topological insulator in graphdiyne
• Spin-group symmetry in magnetic materials with negligible spin-orbit coupling
• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Topological Materials Discovery from Crystal Symmetry
• Material design with the van der Waals stacking of bismuth-halide chains realizing a higher-order topological insulator
• Unsupervised machine learning and band topology
• Evidence of Higher Order Topology in Multilayer WTe${}_2$ from Josephson Coupling through Anisotropic Hinge States
• First Principles Calculations for Topological Quantum Materials
• Band Representations and Topological Quantum Chemistry
• Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne
• Engineering Weyl phases and nonlinear Hall effects in T${}_d$-MoTe${}_2$
• Higher-order Dirac fermions in three dimensions
• Polar and phase domain walls with conducting interfacial states in a Weyl semimetal MoTe2
• ${\mathbb{Z}}_2$-projective translational symmetry protected topological phases
• Fragile Phases As Affine Monoids: Classification and Material Examples
• Symmetry indicators of band topology
• High-throughput search for magnetic and topological order in transition metal oxides
• Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• Atomic limit and inversion-symmetry indicators for topological superconductors
• Purely rotational symmetry-protected topological crystalline insulator $\alpha$-Bi4Br4
• Non-Hermitian band topology with generalized inversion symmetry
• Application of topological quantum chemistry in electrides
• SpaceGroupIrep: A package for irreducible representations of space group
• Computation of topological phase diagram of disordered Pb${}_{1-x}$Sn${}_x$Te using the kernel polynomial method
• Computational Search for Magnetic and Non-magnetic 2D Topological Materials using Unified Spin-orbit Spillage Screening
• Magnetic Weyl semimetal in K${}_2$Mn${}_3$(AsO${}_4$)${}_3$ with the minimum number of Weyl points
• Artificial Intelligence for High-Throughput Discovery of Topological Insulators: the Example of Alloyed Tetradymites
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Two-dimensional topological materials discovery by symmetry-indicator method
• Exhaustive List of Topological Hourglass Band Crossings in 230 Space Groups
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• Topological electronic structure and spin texture of quasi-one-dimensional higher-order topological insulator Bi4Br4
• Machine learning spectral indicators of topology
• Topological Superconductivity in an s-wave Superconductor and Its Implication to Iron-based Superconductors
• Symmetry indicator in non-Hermitian systems
• Buckled honeycomb group-$V$--$S_6$ symmetric $(d-2)$ higher order topological insulators
• Discovery of a hybrid topological quantum state in an elemental solid
• Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
• Symmetry Analysis of Anomalous Floquet Topological Phases
• Location and topology of the fundamental gap in photonic crystals
• Theory of inversion-${\mathbb{Z}}_4$ protected topological chiral hinge states and its applications to layered antiferromagnets
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• Appearance of hinge states in second-order topological insulators via the cutting procedure
• Higher-Order Topological Crystalline Insulating Phase and Quantized Hinge Charge in Topological Electride Apatite
• High-throughput screening for Weyl Semimetals with S${}_4$ Symmetry
• Second-order and real Chern topological insulator in twisted bilayer $\alpha$-graphyne
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• Topological Crystalline Insulators with $C_2$ Rotation Anomaly
• MSGCorep: A package for corepresentations of magnetic space groups
• Double Majorana vortex zero modes in superconducting topological crystalline insulators with surface rotation anomaly
• Facet Dependent Topological Phase Transition in Bi4Br4
• Discovering two-dimensional magnetic topological insulators by machine learning
• Traversing double-well potential energy surfaces: photoinduced concurrent intralayer and interlayer structural transitions in XTe2 (X=Mo, W)
• Topological crystalline insulator state with type-II Dirac fermions in transition metal dipnictides
• Two-dimensional weak-type topological insulators in inversion symmetric crystals
• Third-order charge transport in a magnetic topological semimetal
• Majorana multipole response: General theory and application to wallpaper groups
• Persistence of Monoclinic Crystal Structure in Three-Dimensional Second-Order Topological Insulator Candidate 1T'-MoTe2 Thin Flake without Structural Phase transition
• Effective action approach to the filling anomaly in crystalline topological matter
• Optical bulk-boundary dichotomy in a quantum spin Hall insulator
• Quantum transport evidence of the boundary states and Lifshitz transition in Bi${}_4$Br${}_4$
• Zeros of Green Functions in Topological Insulators
• Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
• Magnetic hourglass fermions: from exhaustive symmetry conditions to high-throughput materials predictions
• Reshaped Weyl fermionic dispersions driven by Coulomb interactions in MoTe2
• Tunable spin Hall and spin Nernst effects in Dirac line-node semimetals XCuYAs (X=Zr, Hf; Y=Si, Ge)
• Topologically Protected Edge States in Triangular Lattices
• Higher-order topological superconductivity in a topological metal 1T${}^{\prime }$-MoTe${}_2$
• Discovery of Ĉ${}_2$ rotation anomaly in topological crystalline insulator SrPb
• Quasi-One-Dimensional Higher-Order Topological Insulators
• BerryEasy: A GPU enabled python package for diagnosis of nth-order and spin-resolved topology in the presence of fields and effects
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• XFe4Ge2 (X = Y, Lu) and Mn3Pt: Filling-enforced magnetic topological metals
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
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• Theory of fractional corner charges in cylindrical crystal shapes
• Excited-state dynamics of structurally characterized crystal of SnxSb1-x
• IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures
• Magneto-optical Conductance of Kane Fermion Gas in Low Frequencies
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• Quantum Coherent Transport of 1D ballistic states in second order topological insulator Bi${}_4$Br${}_4$
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• Confinement Effect Driven Quantum Spin Hall Effect in Monolayer AuTe2Cl
• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals
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