Mathematical analysis

Engineering

Geometry

Combinatorics

Physics

Topology (electrical circuits)

Mathematics

Hermitian matrix

Quantum mechanics

Homogeneous space

Knot theory

Invariant (physics)

Knot (papermaking)

Chemical engineering

Polynomial

Position and momentum space

Physical Review Letters

Topological nodal line semimetals host stable chained, linked, or knotted line degeneracies in momentum space protected by symmetries. In this Letter, we use the Jones polynomial as a general topological invariant to capture the global knot topology of the oriented nodal lines. We show that every possible change in Jones polynomial is attributed to the local evolutions around every point where two nodal lines touch. As an application of our theory, we show that nodal chain semimetals with four touching points can evolve to a Hopf link. We extend our theory to 3D non-Hermitian multiband exceptional line semimetals. Our work provides a recipe to understand the transition of the knot topology for protected nodal lines.Received 16 May 2019Revised 18 March 2020Accepted 20 March 2020DOI:https://doi.org/10.1103/PhysRevLett.124.186402© 2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasTopological phase transitionTopological phases of matterPhysical SystemsNode-line semimetalsTopological materialsCondensed Matter, Materials & Applied Physics

Jones Polynomial and Knot Transitions in Hermitian and non-Hermitian Topological Semimetals