Abstract
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 forms of double diamond structures which realize the nodal links in the momentum space. By examining the evolution of the eigenstate correlations along the closed loops which 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.
Highlights
A nodal link is a special form of a line degeneracy between adjacent bands in the momentum space of a three-dimensional topological crystal
The realization of the nodal link in a dielectric photonic crystal starts with taking the well-known diamond structure[51] and subsequently breaking its several geometrical symmetries as will be explained below
By the inequalities mentioned above, this photonic crystal consists of two inversion symmetric single diamonds, and they do not intersect each other like other bicontinuous structures.[5,12,13,52−55] If A1 = A2 = A3 = 1, the space group of each part becomes Fd3m (No 227), and each diamond is identical to the well-known diamond structure.[51]
Summary
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. 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 analyzed. Despite the abundance of studies on the nodal lines[13,17,32,40,42,50] and the non-Abelian band topology in photonics,[42] there has not been any textbook example on the nodal link. The nonAbelian topological features of the nodal link are characterized by considering a loop that encloses one or more sections of the link and examining the correlations of the eigenstates
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