2017/04/17 by Motohiko Ezawa · 143 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Fermi Gamma-ray Space Telescope #Geometric and Algebraic Topology #Geometry #Hopf algebra #Knot (papermaking) #Knot invariant #Knot theory #Mathematics #Physics #Pure mathematics #Quantum mechanics #Topological Materials and Phenomena #Topology (electrical circuits) #Torus #Trefoil knot #cond-mat.mes-hall #cond-mat.mtrl-sci #cond-mat.quant-gas #hep-th
paper · pdf · doi:10.1103/physrevb.96.041202
published in Physical review. B./Physical review. B 96(4) (American Physical Society) · 4 pages, 6 figures
arxiv created 2017/04/17 · openalex created_date 2017/05/05 · openalex publication_date 2017/07/05 · arxiv updated 2017/09/20 · openalex updated_date 2026/08/05
We propose a type of Hopf semimetal indexed by a pair of numbers (p,q), where the Hopf number is given by pq. The Fermi surface is given by a preimage of the Hopf map, which consists of loops nontrivially linked for a nonzero Hopf number. The Fermi surface forms a torus link, whose examples are a Hopf link indexed by (1,1), Solomon's knot (2,1), a double Hopf link (2,2), and a double trefoil knot (3,2). We may choose p or q to be a half integer, where the Fermi surface is a torus knot, such as a trefoil knot (3/2,1). It is even possible to make the Hopf number an arbitrary rational number, where a semimetal whose Fermi surface forms open strings is generated.