Non-Abelian reciprocal braiding of Weyl points and its manifestation in $\text{ZrTe}$

Abstract

Weyl semimetals in three-dimensional crystals provide the paradigm example of topologically protected band nodes. It is usually taken for granted that a pair of colliding Weyl points annihilate whenever they carry opposite chiral charge. In a stark contrast, here we report that Weyl points in systems symmetric under the composition of time-reversal with a $\pi$-rotation are characterized by a non-Abelian topological invariant. The topological charges of the Weyl points are transformed via braid phase factors which arise upon exchange inside symmetric planes of the reciprocal momentum space. We elucidate this process with an elementary two-dimensional tight-binding model implementable in cold-atoms setups and in photonic systems. In three dimensions, interplay of the non-Abelian topology with point-group symmetry is shown to enable topological phase transitions in which pairs of Weyl points may scatter or convert into nodal-line rings. By combining our theoretical arguments with first-principles calculations, we predict that Weyl points occurring near the Fermi level of zirconium telluride ($\text{ZrTe}$) carry non-trivial values of the non-Abelian charge, and that uniaxial compression strain drives a non-trivial conversion of the Weyl points into nodal lines.

Main text (7 pages, 6 figures + bibliography); Methods (3 pages); Extended Data (7 figures); Supplementary material (15 pages, 8 figures + bibliography)

References in corpus (43)

• Topological Insulators
• Topological insulators and superconductors
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• WannierTools: An open-source software package for novel topological materials
• Type-II Weyl Semimetals
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Crystalline Insulators
• Periodic table for topological insulators and superconductors
• Topological quantum chemistry
• Observation of the chiral anomaly induced negative magneto-resistance in 3D Weyl semi-metal TaAs
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Experimental observation of Weyl points
• Topological orders and Edge excitations in FQH states
• Catalogue of Topological Electronic Materials
• Topological nodal line semimetals
• Weyl points and line nodes in gapless gyroid photonic crystals
• The space group classification of topological band insulators
• Nodal-chain metals
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• All "Magic Angles" Are "Stable" Topological
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
• Experimental Observation of Three-Component 'New Fermions' in Topological Semimetal MoP
• Disclination Loops, Hedgehogs, and All That
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• 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
• Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
• Co-existence of Weyl Fermion and Massless Triply Degenerate Nodal Points
• Bloch state tomography using Wilson lines
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• Three-component fermions with surface Fermi arcs in topological semimetal tungsten carbide
• The translational side of topological band insulators
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Magnetotransport properties of the triply degenerate node topological semimetal tungsten carbide
• Topological Bloch oscillations
• Global band topology of simple and double Dirac-point (semi-)metals
• Conversion rules for Weyl points and nodal lines in topological media
• Optimal Topological Test for Degeneracies of Real Hamiltonians
• Elastic and transport properties of topological semimetal ZrTe

Cited by in corpus (121)

• Topological Non-Hermitian skin effect
• Topological Euler class as a dynamical observable in optical lattices
• Experimental observation of non-Abelian topological charges and bulk-edge correspondence
• Observation of non-Abelian topological semimetals and their phase transitions
• Geometric approach to fragile topology beyond symmetry indicators
• Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
• Topological correspondence between magnetic space group representations
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Bicircular light tuning of magnetic symmetry and topology in Dirac semimetal Cd${}_3$As${}_2$
• Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems
• Topological acoustic triple point
• Four-band non-Abelian topological insulator and its experimental realization
• Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Minimal non-abelian nodal braiding in ideal metamaterials
• Subdimensional topologies, indicators and higher order phases
• Experimental observation of non-Abelian earring nodal links in phononic crystals
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• From triple-point materials to multiband nodal links
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Synthetic non-Abelian gauge fields for non-Hermitian systems
• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Braid Protected Topological Band Structures with Unpaired Exceptional Points
• Degenerate topological line surface phonons in quasi-1D double helix crystal SnIP
• Quantized Integrated Shift Effect in Multigap Topological Phases
• Optical manifestations and bounds of topological Euler class
• Topological Euler insulators
• Non-Abelian charged nodal links in dielectric photonic crystal
• Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence
• $N$-band Hopf insulator
• Topological continuum charges of acoustic phonons in 2D
• Intrinsic Magnetic Topological Materials
• Non-Abelian tensor Berry connections in multi-band topological systems
• Euler Obstructed Cooper Pairing: Nodal Superconductivity and Hinge Majorana Zero Modes
• Phase transitions of non-Abelian charged nodal links in a spring-mass system
• Non-Abelian Hopf-Euler insulators
• Euler Obstructed Cooper Pairing in Twisted Bilayer Graphene: Nematic Nodal Superconductivity and Bounded Superfluid Weight
• Landau Levels of the Euler Class Topology
• Absence of topological protection of the interface states in ${\mathbb{Z}}_2$ photonic crystals
• Massless multifold Hopf semimetals
• Theory of polarization textures in crystal supercells
• Quantum Valley Hall effect without Berry curvature
• Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• Unsupervised Learning of Topological Non-Abelian Braiding in Non-Hermitian Bands
• Non-Abelian Braiding of Topological Edge Bands
• Chirality flip of Weyl nodes and its manifestation in strained MoTe${}_2$
• Nested-sphere description of the N-level Chern number and the generalized Bloch hypersphere
• Weyl points on non-orientable manifolds
• Interferometry of non-Abelian band singularities and Euler class topology
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Photonic nodal lines with quadrupole Berry curvature distribution
• Machine Learning of Knot Topology in Non-Hermitian Band Braids
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Real Hopf Insulator
• Quantum optics measurement scheme for quantum geometry and topological invariants
• Triple nodal points characterized by their nodal-line structure in all magnetic space groups
• Fermi-arc metals
• Bulk-edge correspondence of Stiefel-Whitney and Euler insulators through the entanglement spectrum and cutting procedure
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Wave packet dynamics and edge transport in anomalous Floquet topological phases
• Projected spin texture as a bulk indicator of fragile topology
• Demonstration of non-Abelian frame charge flow in photonic crystals
• Hermitian Topologies originating from non-Hermitian braidings
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Anomalous geometric transport signatures of topological Euler class
• Exact projected entangled pair ground states with topological Euler invariant
• Synthetic non-Abelian topological charges in ultracold atomic gases
• Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry
• Andreev reflection in Euler materials
• Textured Exciton Insulators
• Braiding topology of symmetry-protected degeneracy points in non-Hermitian systems
• Revealing the topological phase diagram of ZrTe${}_5$ using the complex strain fields of microbubbles
• Gapping fragile topological bands by interactions
• Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States
• The quest and hope of Majorana zero modes in topological superconductor for fault-tolerant quantum computing: an introductory overview
• Rigidity of topological invariants to symmetry breakings
• Observing the nodal-line conversion determined by the relative homotopy
• Quantum geometry of bosonic Bogoliubov quasiparticles
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
• Optical signatures of Euler superconductors
• Probing fragile topology with a screw dislocation
• Floquet non-Abelian topological charges and edge states
• Second Euler number in four dimensional synthetic matter
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
• Punctured-Chern topological invariants for semi-metallic bandstructures
• Stability of Weyl node merging processes under symmetry constraints
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• Layer Construction of Three-Dimensional Z2 Monopole Charge Nodal Line Semimetals and prediction of the abundant candidate materials
• Observation of Braid-Protected Unpaired Exceptional Points
• Polarization textures in crystal supercells with topological bands
• Geometric semimetals and their simulation in synthetic matter
• Topological Dynamics and Correspondences in Composite Exceptional Rings
• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
• Unremovable linked nodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekulé texture
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Breakdown of boundary criticality and exotic topological semimetals in $\mathcal{P}\mathcal{T}$-invariant systems
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Topological insulators and geometry of vector bundles
• Euler band topology in superfluids and superconductors
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Floquet composite Dirac semimetals
• Fermionic atoms in a spin-dependent optical lattice potential: topological insulators with broken time-reversal symmetry
• Non-Abelian interference of topological edge states
• Coupled-wire construction of non-Abelian higher-order topological phases
• Orbital magnetization reveals multiband topology
• Hinge modes of three-dimensional Euler insulators
• Semimetals without correspondence between the topological charge of nodal line/surface and Fermi arc
• Emergence of Nodal-Knot Transitions by Disorder
• Three-dimensional spinless Euler insulators with rotational symmetry
• Non-adiabatic corrections to chiral charge pumping in topological nodal semimetals
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Non-abelian Geometric Quantum Energy Pump