Conversion rules for Weyl points and nodal lines in topological media

Abstract

According to a widely-held paradigm, a pair of Weyl points with opposite chirality mutually annihilate when brought together. In contrast, we show that such a process is strictly forbidden for Weyl points related by a mirror symmetry, provided that an effective two-band description exists in terms of orbitals with opposite mirror eigenvalue. Instead, such a pair of Weyl points convert into a nodal loop inside a symmetric plane upon the collision. Similar constraints are identified for systems with multiple mirrors, facilitating previously unreported nodal-line and nodal-chain semimetals that exhibit both Fermi-arc and drumhead surface states. We further find that Weyl points in systems symmetric under a $\pi$-rotation composed with time-reversal are characterized by an additional integer charge that we call helicity. A pair of Weyl points with opposite chirality can annihilate only if their helicities also cancel out. We base our predictions on topological crystalline invariants derived from relative homotopy theory, and we test our predictions on simple tight-binding models. The outlined homotopy description can be directly generalized to systems with multiple bands and other choices of symmetry.

arXiv commentMain text: 4 pages with 4 figures. Supplement (submitted as ancillary file): 19 pages with 9 figures

References in corpus (79)

• Topological Insulators
• Topological insulators and superconductors
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Classification of topological quantum matter with symmetries
• Type-II Weyl Semimetals
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• First observation of Spin-Momentum Helical Locking in Bi2Se3 and Bi2Te3, demonstration of Topological-Order at 300K and a realization of topological-transport-regime
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Periodic table for topological insulators and superconductors
• Dirac semimetal in three dimensions
• Experimental discovery of Weyl semimetal TaAs
• Topological nodal semimetals
• Topological quantum chemistry
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• Spin Transfer Torque Generated by the Topological Insulator Bi_2Se_3
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological nodal line semimetals with and without spin-orbital coupling
• Dirac Line Nodes in Inversion Symmetric Crystals
• Topological Nodal Line Semimetal and Dirac Semimetal State in Antiperovskite Cu${}_3$PdN
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Dirac Cone Protected by Non-Symmorphic Symmetry and 3D Dirac Line Node in ZrSiS
• Topological nodal line semimetals
• Recent developments in transport phenomena in Weyl semimetals
• Dirac Semimetals in Two Dimensions
• The space group classification of topological band insulators
• Control over topological insulator photocurrents with light polarization
• Topological classification of crystalline insulators through band structure combinatorics
• Nodal-chain metals
• The Zak phase and the existence of edge states in graphene
• Topology of crystalline insulators and superconductors
• Wannier representation of Z_2 topological insulators
• MoTe2: A Type-II Weyl Topological Metal
• Spin-orbit-free Weyl-loop and Weyl-point semimetals in a stable three-dimensional carbon allotrope
• Nodal surface semimetals: Theory and material realization
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Drumhead Surface States and Topological Nodal-Line Fermions in TlTaSe2
• Stability of Fermi Surfaces and K-Theory
• Nodal-link semimetals
• Flat bands in topological media
• Node-Surface and Node-Line Fermions From Nonsymmorphic Lattice Symmetries
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Symmetry-protected ideal Weyl semimetal in HgTe-class materials
• Confinement-induced Berry phase and helicity-dependent photocurrents
• Bogoliubov Fermi surfaces in superconductors with broken time-reversal symmetry
• Towards Three-Dimensional Weyl-SurfaceSemimetals in Graphene Networks
• Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
• Topological semimetals with double-helix nodal link
• Nodal-knot semimetals
• Topological Classification and Stability of Fermi Surfaces
• Topological Dirac Nodal Lines and Surface Charges in fcc Alkaline Earth Metals
• From Nodal Chain Semimetal To Weyl Semimetal in HfC
• Unified theory of PT and CP invariant topological metals and nodal superconductors
• Hourglass Dirac Chain Metal in Rhenium Dioxide
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• Topological Semimetals carrying Arbitrary Hopf Numbers: Hopf-Link, Solomon's-Knot, Trefoil-Knot and Other Semimetals
• Nonsymmorphic symmetry-required band crossings in topological semimetals
• Topological Dirac Nodal-net Fermions in AlB${}_2$-type TiB${}_2$ and ZrB${}_2$
• Dirac and nodal line magnons in three-dimensional antiferromagnets
• Composite Weyl nodes stabilized by screw symmetry with and without time reversal
• Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals
• Nexus and Dirac lines in topological materials
• Topological Blount's theorem of odd-parity superconductors
• Weyl-link semimetals
• Topological charges of three-dimensional Dirac semimetals with rotation symmetry
• Pseudospin Vortex Ring with a Nodal Line in Three Dimensions
• Weyl nodal surfaces
• Observation of a nodal chain with Dirac surface states in TiB2
• Symmorphic intersecting nodal rings in semiconducting layers
• Double helix nodal line superconductor
• Topological density-wave states in a particle-hole symmetric Weyl metal
• Topological Crystalline Metal in Orthorhombic Perovskite Iridates

Cited by in corpus (36)

• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Non-Abelian band topology in noninteracting metals
• Non-Abelian reciprocal braiding of Weyl points and its manifestation in $\text{ZrTe}$
• Geometric approach to fragile topology beyond symmetry indicators
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Room temperature two-dimensional antiferromagnetic Weyl semimetal CrO with giant spin-splitting and spin-momentum locked transport
• Mixed topological semimetals driven by orbital complexity in two-dimensional ferromagnets
• Topological carbon materials: a new perspective
• Photonic ${\mathbb{Z}}_2$ topological Anderson insulators
• Multicellularity of delicate topological insulators
• Topological semimetals in the SnTe material class: Nodal lines and Weyl points
• Subdimensional topologies, indicators and higher order phases
• Three-dimensional Chiral Lattice Fermion in Floquet Systems
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• From triple-point materials to multiband nodal links
• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Braid Protected Topological Band Structures with Unpaired Exceptional Points
• Massless multifold Hopf semimetals
• Universal higher-order bulk-boundary correspondence of triple nodal points
• ${\mathbb{Z}}_2$ Spin Hopf Insulator: Helical Hinge States and Returning Thouless Pump
• Evidencing non-Bloch dynamics in temporal topolectrical circuits
• Large Josephson current in Weyl nodal loop semimetals due to odd-frequency superconductivity
• Floquet and Anomalous Floquet Weyl Semimetals
• Extrinsic and Intrinsic Nonlinear Hall Effects across Berry-Dipole Transitions
• Photonic nodal lines with quadrupole Berry curvature distribution
• Alice string in Non-Hermitian Systems
• Weyl singularities in polaritonic multi-terminal Josephson junctions
• Unique surface-state connection between Weyl and nodal ring fermions in ferromagnetic material Cs2MoCl6
• Berry-dipole Semimetals
• Observing the nodal-line conversion determined by the relative homotopy
• Linking structures of doubly charged nodal surfaces in centrosymmetric superconductors
• Dissipationless transport signature of topological nodal lines
• Topological charge distributions of an interacting two-spin system
• Non-adiabatic corrections to chiral charge pumping in topological nodal semimetals
• Tunable SSH model in ferromagnetic systems