Topological semimetals carrying arbitrary Hopf numbers: Fermi surface topologies of a Hopf link, Solomon's knot, trefoil knot, and other linked nodal varieties Article Swipe

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Mathematics Knot (papermaking) Fermi Gamma-ray Space Telescope Knot theory Trefoil knot Torus Hopf algebra Knot invariant Topology (electrical circuits) Combinatorics Pure mathematics Physics Quantum mechanics Algebra over a field Geometry Chemical engineering Engineering

Motohiko Ezawa ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.1103/physrevb.96.041202 · OA: W2608891415

We propose a new type of Hopf semimetals indexed by a pair of numbers\n$(p,q)$, where the Hopf number is given by $pq$. The Fermi surface is given by\nthe preimage of the Hopf map, which is nontrivially linked for a nonzero Hopf\nnumber. The Fermi surface forms a torus link, whose examples are the Hopf link\nindexed by $(1,1)$, the Solomon's knot $(2,1)$, the double Hopf-link $(2,2)$\nand the double trefoil-knot $(3,2)$. We may choose $p$ or $q$ as a half\ninteger, where torus-knot Fermi surfaces such as the trefoil knot $(3/2,1)$ are\nrealized. It is even possible to make the Hopf number an arbitrary rational\nnumber, where a semimetal whose Fermi surface forms open strings is generated.\n