Pseudospin Vortex Ring with a Nodal Line in Three Dimensions

Abstract

We present a model of a topological semimetal in three dimensions (3D) whose energy spectrum exhibits a nodal line acting as a vortex ring; this in turn is linked by a pseudospin structure akin to that of a smoke ring. Contrary to a Weyl point node spectrum, the vortex ring gives rise to skyrmionic pseudospin patterns in cuts on both sides of the nodal ring plane; this pattern covers the full Brillouin zone, thus leading to a new, `maximal', anomalous Hall effect in a 3D semimetal. Tuning a model parameter shrinks the vortex ring until it vanishes, giving way to a pair of Weyl nodes of opposite chirality. This establishes a connection between two distinct momentum-space topologies - that of a vortex ring (a circle of singularity) and a monopole-anti-monopole pair (two point singularities). We present the model both as a low-energy continuum and a two-band tight-binding lattice model. Its simplicity permits an analytical computation of its Landau level spectrum.

5 pages, 5 figures, appendix (4 pages); accepted for publication in Phys. Rev. Lett

References in corpus (16)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Unconventional Integer Quantum Hall effect in graphene
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological Node-Line Semimetal in Three Dimensional Graphene Networks
• Detecting Topological Currents in Graphene Superlattices
• Nodal-chain metals
• Topological Semimetals Predicted from First-principles Calculations
• Potential ring of Dirac nodes in a new polymorph of Ca${}_3$P${}_2$
• Line of Dirac Nodes in Hyper-Honeycomb Lattices
• Tunable Weyl Points in Periodically Driven Nodal Line Semimetals
• Friedel oscillations due to Fermi arcs in Weyl semimetals
• Tunable Line Node Semimetals
• Topologically Protected Zero Modes in Twisted Bilayer Graphene
• Type-II Weyl cone transitions in driven semimetals
• Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems

Cited by in corpus (43)

• Topological quantum matter with cold atoms
• Nodal-link semimetals
• Nonsymmorphic-symmetry-protected hourglass Dirac loop, nodal line, and Dirac point in bulk and monolayer $X_3$SiTe${}_6$ ($X=$ Ta, Nb)
• Topological Lifshitz transitions
• Topolectric circuits: Theory and construction
• Optical Signatures of Dirac Nodal-lines in NbAs${}_2$
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Realistic Floquet semimetal with exotic topological linkages between arbitrarily many nodal loops
• Interacting line-node semimetal: Proximity effect and spontaneous symmetry breaking
• A Class of topological nodal rings and its realization in carbon networks
• Conversion rules for Weyl points and nodal lines in topological media
• Crossing-Line-Node Semimetals: General Theory and Application to Rare-Earth Trihydrides
• Topological Materials Discovery using Electron Filling Constraints
• Quantum Oscillations in Nodal Line Systems
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Almost ideal nodal-loop semimetal in monoclinic CuTeO${}_3$ material
• Generating quantum multi-criticality in topological insulators by periodic driving
• Topological Gapless Matters in Three-dimensional Ultracold Atomic Gases
• Topological and trivial magnetic oscillations in nodal loop semimetals
• Observation of Effective Pseudospin Scattering in ZrSiS
• Mirror Protected Multiple Nodal Line Semimetals and Material Realization
• Engineering topological phases with a three-dimensional nodal-loop semimetal
• Weyl solitons in three-dimensional optical lattices
• $2\pi$-flux loop semimetals
• Real spin and pseudospin topologies in the noncentrosymmetric topological nodal-line semimetal CaAgAs
• Engineering second-order nodal-line semimetals by breaking $\mathcal{P}\mathcal{T}$ symmetry and periodic driving
• 3D Quantum Anomalous Hall Effect in Hyperhoneycomb Lattices
• Signature of topological non-trivial band structure in Ta${}_3$SiTe${}_6$
• Imbert-Fedorov shift in pseudospin-$N/2$ semimetals and nodal-line semimetals
• $R$RuB${}_2$ ($R$=Y, Lu), topological superconductor candidates with hourglass-type Dirac ring
• Superconductivity and a van Hove singularity confined to the surface of a topological semimetal
• Trigonal warping induced terraced spin texture and nearly perfect spin polarization in graphene with Rashba effect
• Spin and charge transport in topological nodal-line semimetals
• Elastic gauge fields and zero-field 3D quantum Hall effect in hyperhoneycomb lattices
• Topological Singularities in Metasurface Scattering Matrices: From Nodal Lines to Exceptional Lines
• Triply degenerate nodal lines in topological and non-topological metals
• Characterization of Lifshitz transitions in topological nodal line semimetals
• Quantum Oscillation and Landau-Zener transition in Untilted Nodal line semimetals under a time-periodic magnetic field
• Nodal-line semimetals and their variance
• Fermi Level Fluctuations, Reduced Effective Masses and Zeeman Effect during Quantum Oscillations in Nodal Line Semimetals
• Topological Fermi-arc-like surface states in Kramers nodal line metals
• Cartesian Nodal Lines and Magnetic Kramers Weyl Nodes in Spin-Split Antiferromagnets
• Non-adiabatic corrections to chiral charge pumping in topological nodal semimetals