Non-Abelian Charged Nodal Links in a Dielectric Photonic Crystal

A nodal link is a special form of a line degeneracy (a nodal line) between adjacent bands in the momentum space of a three-dimensional topological crystal. Unlike nodal chains or knots, a nodal link consists of two or more mutually linked rings that do not touch each other. Recent studies on non-Abelian band topology revealed that the topological charges of the nodal links can have the properties of quaternions. However, a photonic crystal that has a nodal link with non-Abelian charges has not been reported. Here, we propose dielectric photonic crystals in the form of double diamond structures that realize the nodal links in the momentum space. By examining the evolution of the eigenstate correlations along closed loops that enclose the nodal line(s) of the links, their non-Abelian topological charges are also analyzed. The proposed design scheme and theoretical approach in this work will allow for experimental observation of photonic non-Abelian charges in purely dielectric materials and facilitate the control of the degeneracy in complex photonic structures.

Automated summary

The article introduces a special form of nodal link in the momentum space of three-dimensional topological crystals and proposes a dielectric photonic crystal structure to realize nodal links. The evolution of eigenstate correlations along closed loops enclosing the nodal lines is examined to analyze the non-Abelian topological charges of the nodal links. This work's design scheme and theoretical approach aim to enable experimental observation of photonic non-Abelian charges and control degeneracy in complex photonic structures using purely dielectric materials.