Nodal-knot semimetals

Abstract

Topological nodal-line semimetals are characterized by one-dimensional lines of band crossing in the Brillouin zone. In contrast to nodal points, nodal lines can be in topologically nontrivial configurations. In this paper, we study the simplest topologically nontrivial forms of nodal line, namely, a single nodal line taking the shape of a knot in the Brillouin zone. We introduce a generic construction for various "nodal-knot semimetals", which yields the simplest trefoil nodal knot and other more complicated nodal knots in the Brillouin zone. The knotted-unknotted transitions by nodal-line reconnections are also studied. Our work brings the knot theory to the subject of topological semimetals.

7 pages, 5 figures. Figure quality improved.

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• Observation of non-Abelian nodal links in photonics
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• Phononic Weyl Nodal Straight Lines in High-Temperature Superconductor MgB${}_2$
• Imaging nodal knots in momentum space through topolectrical circuits
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• Simulating Exceptional Non-Hermitian Metals with Single-Photon Interferometry
• Non-Hermitian Topological Phases: Principles and Prospects
• Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems
• Hopf-link multi-Weyl-loop topological semimetals
• Systematic investigation of emergent particles in type-III magnetic space groups
• Realization of a Hopf insulator in circuit systems
• Observation of a nodal chain with Dirac surface states in TiB2
• Conversion rules for Weyl points and nodal lines in topological media
• Complete classification of band nodal structures
• Classification of Exceptional Nodal Topologies Protected by $\mathcal{P}\mathcal{T}$ Symmetry
• From triple-point materials to multiband nodal links
• Untying links through anti-parity-time-symmetric coupling
• Magnetic and electronic properties of a topological nodal line semimetal candidate: HoSbTe
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• Demonstration of non-Abelian frame charge flow in photonic crystals
• Cyclotron orbit knot and tunable-field quantum Hall effect
• Doubling Theorem and Boundary States of Five-Dimensional Weyl Semimetal
• Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines
• Symmetry-protected Spinful Magnetic Weyl Nodal Loops and Multi-Weyl Nodes in $5d^n$ Cubic Double Perovskites $(n=1,2)$
• Magnetotransport Properties and Fermi Surface Topology of Nodal line Semimetal InBi
• Novel Family of Topological Semimetals with Butterfly-like Nodal Lines
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