Circumventing the no-go theorem: A single Weyl point surrounded by nodal walls

Abstract

Despite of a rapidly expanding inventory of possible crystalline Weyl semimetals, all of them are constrained by the Nielsen-Ninomiya no-go theorem, namely, that left- and right-handed Weyl points appear in pairs. With time-reversal (T) symmetry, an even stronger version holds for the semimetals, i.e., all eight time-reversal-invariant points in the Brillouin zone (BZ) simultaneously host Weyl points or not. However, all the well-known conclusions from the no-go theorem are implicitly within the current framework of topological semimetals, and in this work, we shall go beyond it by exploring composites of topological metal and semimetal phases. Guided by crystal symmetry and T symmetry, we propose a new topological phase of T-invariant crystalline metal, where a single Weyl point resides at the center of the BZ, surrounded by nodal walls spreading over the entire BZ boundary. In other words, a single Weyl point is realized with the no-go theorem being circumvented. Meanwhile, the Fermi arc surface states, considered as a hallmark of Weyl semimetals, do not appear for this new composite topological phase. We show that this phase can be realized for space group 19 and 92, with and without spin-orbit coupling, respectively.

arXiv comment12 pages, 4 figures

References in corpus (72)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Weyl Semimetal in a Topological Insulator Multilayer
• Topological Materials: Weyl Semimetals
• Experimental discovery of Weyl semimetal TaAs
• Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• A Method for Simulating Chiral Fermions on the Lattice
• Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal NbP
• Experimental observation of Weyl points
• Observation of Weyl nodes in TaAs
• Topolectrical circuit realization of topological corner modes
• Topological Bands for Ultracold Atoms
• Acoustic higher-order topological insulator on a Kagome lattice
• Quantum Hall effects in a Weyl Semi-Metal: possible application in pyrochlore Iridates
• Topological Node-Line Semimetal in Three Dimensional Graphene Networks
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
• Topolectrical circuits
• The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi
• Quantum Oscillations from Surface Fermi-Arcs in Weyl and Dirac Semi-Metals
• Electromagnetic Response of Weyl Semimetals
• Topological quantum properties of chiral crystals
• Experimental discovery of a topological Weyl semimetal state in TaP
• MoTe2: A Type-II Weyl Topological Metal
• Transport evidence for Fermi-arc mediated chirality transfer in the Dirac semimetal Cd${}_3$As${}_2$
• Time-Reversal-Breaking Weyl Fermions in Magnetic Heusler Alloys
• Realization of a three-dimensional photonic topological insulator
• Nodal surface semimetals: Theory and material realization
• Chiral gauge field and axial anomaly in a Weyl semi-metal
• Dirac and Weyl Superconductors in Three Dimensions
• Node-Surface and Node-Line Fermions From Nonsymmorphic Lattice Symmetries
• Chiral Anomaly and Diffusive Magnetotransport in Weyl Metals
• Predicted Unusual Magnetoresponse in Type-II Weyl Semimetals
• Symmetry-protected ideal Weyl semimetal in HgTe-class materials
• BCS-BEC Crossover and Topological Phase Transition in 3D Spin-Orbit Coupled Degenerate Fermi Gases
• Fermi arcs and their topological character in the candidate type-II Weyl semimetal MoTe2
• Thermoelectric properties of Weyl and Dirac semimetals
• Towards Three-Dimensional Weyl-SurfaceSemimetals in Graphene Networks
• Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
• Quantum transport of disordered Weyl semimetals at the nodal point
• Disorder and metal-insulator transitions in Weyl semimetals
• From Nodal Chain Semimetal To Weyl Semimetal in HfC
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Ideal Weyl semimetals in the chalcopyrites CuTlSe2, AgTlTe2, AuTlTe2 and ZnPbAs2
• Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups
• Nodal Loop and Nodal Surface States in Ti3Al Family Materials
• Topological Imbert-Fedorov shift in Weyl semimetals
• Topological Invariants of Metals and Related Physical Effects
• RKKY interaction of magnetic impurities in Dirac and Weyl semimetals
• Spin-Orbit Semimetals in the Layer Groups
• Quadratic and Cubic Nodal Lines Stabilized by Crystalline Symmetry
• Anomalous Phase Shift of Quantum Oscillations in 3D Topological Semimetals
• Magnetic tunneling induced Weyl node annihilation in TaP
• Weak Topological Insulators and Composite Weyl Semimetals: $\beta$-Bi${}_4$X${}_4$ (X=Br, I)
• Chirality Hall Effect in Weyl Semimetals
• Topological responses from chiral anomaly in multi-Weyl semimetals
• Observation of Fermi Arcs in non-Centrosymmetric Weyl Semi-metal Candidate NbP
• The Dirac-Weyl semimetal: Coexistence of Dirac and Weyl fermions in polar hexagonal $ABC$ crystals
• Anisotropic Weyl Fermions from Quasiparticle Excitation Spectrum of a 3D Fulde-Ferrell Superfluid
• Electronic Cooling in Weyl and Dirac Semimetals
• Density response in Weyl metals
• Heavy Weyl fermion state in CeRu${}_4$Sn${}_6$
• Emulating topological chiral magnetic effects in artificial Weyl semimetals
• Three-dimensional Chiral Lattice Fermion in Floquet Systems
• Circular phonon dichroism in Weyl semimetals
• Weyl Superfluidity in a Three-dimensional Dipolar Fermi Gas
• Disordered Weyl semimetals and their topological family

Cited by in corpus (36)

• Ferromagnetic hybrid nodal loop and switchable type-I and type-II Weyl fermions in two-dimension
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Higher-order Dirac fermions in three dimensions
• MagneticTB: A package for tight-binding model of magnetic and non-magnetic materials
• ${\mathbb{Z}}_2$-projective translational symmetry protected topological phases
• Symmetry-enforced topological nodal planes at the Fermi surface of a chiral magnet
• The gauge-field extended $k\cdot p$ method and novel topological phases
• Magnetic higher-order nodal lines
• Two-dimensional topological semimetals
• Charge-4 Weyl point: Minimum lattice model and chirality-dependent properties
• Symmetry-enforced ideal lantern-like phonons in ternary nitride Li${}_6$WN${}_4$
• Planar Hall effect in topological Weyl and nodal line semimetals
• Single Pair of Weyl Points in Nonmagnetic Crystals
• Symmetry-enforced band crossings in tetragonal materials: Dirac and Weyl degeneracies on points, lines, and planes
• Observation of a singular Weyl point surrounded by charged nodal walls in PtGa
• Recipe for single-pair-Weyl-points phonons carrying the same chiral charges
• Network of topological nodal planes, multifold degeneracies, and Weyl points in CoSi
• Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery
• Double Dirac Nodal Line Semimetal with Torus Surface State
• Intersecting topological nodal ring and nodal wall states in superhard superconductor FeB4
• Type-II topological metals
• Weyl points on non-orientable manifolds
• Triple nodal points characterized by their nodal-line structure in all magnetic space groups
• Weyl Nodal Line-Surface Half-metal in CaFeO${}_3$
• Alice string in Non-Hermitian Systems
• Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams
• Fermi surface of the chiral topological semimetal CoSi
• Giant Chern number of a Weyl nodal surface without upper limit
• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• Coexistent topological and chiral phonons in chiral RhGe: An ab initio study
• Tensor Theory for Higher Dimensional Chern Insulators with Large Chern Numbers
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• Orbital enhanced intrinsic nonlinear planar Hall effect for probing topological phase transition in CuTlSe${}_2$
• Quantum geometry and low-frequency optical conductivity of nodal planes
• Three-nodal surface phonons in solid-state materials: Theory and material realization
• Fermi surface and topology of multiband superconductor BeAu