Multifold nodal points in magnetic materials

Abstract

We describe the symmetry protected nodal points that can exist in magnetic space groups and show that only 3-, 6-, and 8-fold degeneracies are possible (in addition to the 2- and 4-fold degeneracies that have already been studied.) The 3- and 6-fold degeneracies are derived from "spin-1" Weyl fermions. The 8-fold degeneracies come in different flavors. In particular, we distinguish between 8-fold fermions that realize non-chiral "Rarita-Schwinger fermions" and those that can be described as four degenerate Weyl fermions. We list the (magnetic and non-magnetic) space groups where these exotic fermions can be found. We further show that in several cases, a magnetic translation symmetry pins the Hamiltonian of the multifold fermion to an idealized exactly solvable point that is not achievable in non-magnetic crystals without fine-tuning. Finally, we present known compounds that may host these fermions and methods for systematically finding more candidate materials.

arXiv commentv2: published version

References in corpus (69)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Dirac semimetal in three dimensions
• Experimental discovery of Weyl semimetal TaAs
• Topological nodal semimetals
• Topological quantum chemistry
• Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class
• Observation of the chiral anomaly induced negative magneto-resistance in 3D Weyl semi-metal TaAs
• Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd${}_3$As${}_2$
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• The (High Quality) Topological Materials In The World
• Observation of Weyl nodes in TaAs
• Discovery of a Weyl Fermion semimetal state in NbAs
• Topological nodal line semimetals with and without spin-orbital coupling
• Catalogue of Topological Electronic Materials
• Large anomalous Hall effect driven by non-vanishing Berry curvature in non-collinear antiferromagnetic Mn3Ge
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Dirac Line Nodes in Inversion Symmetric Crystals
• Topological Nodal Line Semimetal and Dirac Semimetal State in Antiperovskite Cu${}_3$PdN
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Quantized circular photogalvanic effect in Weyl semimetals
• Evidence for Magnetic Weyl Fermions in a Correlated Metal
• The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi
• Nodal-chain metals
• Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals
• Topological quantum properties of chiral crystals
• Multiple types of topological fermions in transition metal silicides
• Large Fermi Arcs in Unconventional Weyl Semimetal RhSi
• Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn
• Discovery of topological chiral crystals with helicoid arc states
• Topological semi-metals with line nodes and drumhead surface states
• New classes of chiral topological nodes with non-contractible surface Fermi arcs in CoSi
• Time-Reversal-Breaking Weyl Fermions in Magnetic Heusler Alloys
• Double Dirac Semimetals in Three Dimensions
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Potential ring of Dirac nodes in a new polymorph of Ca${}_3$P${}_2$
• Drumhead Surface States and Topological Nodal-Line Fermions in TlTaSe2
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Node-Surface and Node-Line Fermions From Nonsymmorphic Lattice Symmetries
• Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP
• Chiral Topological Semimetal with Multifold Band Crossings and Long Fermi arcs
• Semimetal and Topological Insulator in Perovskite Iridates
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• 3D Dirac semimetals: current materials, design principles and predictions of new materials
• Topological surface Fermi arcs in the magnetic Weyl semimetal Co${}_3$Sn${}_2$S${}_2$
• Chiral Optical Response of Multifold Fermions
• Negative longitudinal magnetoresistance in Dirac and Weyl metals
• Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals
• Room-temperature magnetic topological semimetal state in half-metallic Heusler Co${}_2$TiX (X=Si, Ge, or Sn)
• Bulk Dirac points in distorted spinels
• Are the double Fermi arcs of Dirac semimetals topologically protected?
• Tunable Weyl and Dirac states in the nonsymmorphic compound $\mathbf{CeSbTe}$
• Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups
• The chiral anomaly factory: Creating Weyl fermions with a magnetic field
• Hydrodynamic theory of thermoelectric transport and negative magnetoresistance in Weyl semimetals
• Prediction of a magnetic Weyl semimetal without spin-orbit coupling and strong anomalous Hall effect in the Heusler compensated ferrimagnet Ti2MnAl
• Discovery of coexisting Dirac and triply degenerate magnons in a three-dimensional antiferromagnet
• Filling-enforced Magnetic Dirac Semimetals in Two Dimensions
• Global band topology of simple and double Dirac-point (semi-)metals
• Rarita-Schwinger-Weyl semimetal in Jeff=3/2 electron systems
• Semimetal with both Rarita-Schwinger-Weyl and Weyl excitations
• Strong anomalous Nernst effect in collinear magnetic Weyl semimetals without net magnetic moments
• Topological Materials Discovery using Electron Filling Constraints
• $\beta$-CuI: a Dirac semimetal without surface Fermi arcs
• Magnetic order and transitions in the spin-web compound Cu3TeO6
• On the possibility of magnetic Weyl fermions in non-symmorphic compound PtFeSb

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• High-throughput calculations of magnetic topological materials
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• Perovskite-type YRh${}_3$B with multiple types of nodal point and nodal line states
• Spin Hall and Edelstein Effects in Novel Chiral Noncollinear Altermagnets
• Realization of Practical Eightfold Fermions and Fourfold van Hove Singularity in TaCo${}_2$Te${}_2$
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• Spin-momentum locking from topological quantum chemistry: applications to multifold fermions
• High-degeneracy points protected by site-permutation symmetries
• Topological Circular Dichroism in Chiral Multifold Semimetals
• Charge Conservation Beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids
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• Kramers nodal lines in intercalated TaS${}_2$ superconductors
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• Unpaired topological triply degenerate point for spin-tensor-momentum-coupled ultracold atoms
• A Hamiltonian Approach for Obtaining Irreducible Projective Representations and the $k\cdot p$ Perturbation for Anti-unitary Symmetry Groups
• Unusual Magnetotransport from two dimensional Dirac Fermions in Pd${}_3$Bi${}_2$Se${}_2$
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• Tunable chiral symmetry breaking in symmetric Weyl materials
• Infrared fixed points of higher-spin fermions in topological semimetals
• Anomalous Hall effect in the antiferromagnetic Weyl semimetal SmAlSi
• Magnetic Photocurrents in Multifold Weyl Fermions
• Physical properties of RhGe and CoGe single crystals synthesized under high pressure
• Optical Response from Charge-Density Waves in Weyl Semimetals
• Topological properties of domain walls in antiferromagnetic topological insulators