Hunting topological nodal line semimetals with nontrivial links and knots attracts great interests and remains a difficult task in the condensed matter community.  Encouraged by the recent discovery of the topological nodal chain semimetals, we propose the realization of the exotic link and knot semimetals by considering the evolution of the nodal chain semimetals.  Borrowing the idea of the knot theory, we use the Jones polynomial as a general topological invariant to capture the oriented nodal lines in the semimetals. Every possible change in Jones polynomial describes 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 and provide a recipe to understand the knot topology transition for protected nodal lines.

Reference:
Zhesen Yang, Ching-Kai Chiu, Chen Fang, and Jiangping Hu, Physical Review Letters 124 (18), 186402 (2020) (Editors’ Suggestion)