Abstract
Nodal lines are degeneracies formed by crossing bands in three-dimensional momentum space. Interestingly, these degenerate lines can chain together via touching points and manifest as nodal chains. These nodal chains are usually embedded in two orthogonal planes and protected by the corresponding mirror symmetries. Here, we propose and demonstrate an in-plane nodal chain in photonics, where all chained nodal lines coexist in a single mirror plane instead of two orthogonal ones. The chain point is stabilized by the intrinsic symmetry that is specific to electromagnetic waves at the Г point of zero frequency. By adding another mirror plane, we find a nodal ring that is constructed by two higher bands and links with the in-plane nodal chain. The nodal link in momentum space exhibits non-Abelian characteristics on a C2T - invariant plane, where admissible transitions of the nodal link structure are determined by generalized quaternion charges. Through near-field scanning measurements of bi-anisotropic metamaterials, we experimentally mapped out the in-plane nodal chain and nodal link in such systems.
Highlights
Topological photonics has attracted a lot of attention recently[1,2]
We show that photonic intrinsic symmetry can stabilize the chain point
The mirror eigenvalues of the eigenstates on the ky = kz = 0 line have the same (+) sign across the chain point, which indicate that the in-plane chain point is no longer stable since the symmetry eigenvalue sign change going across that point no longer exists
Summary
Topological photonics has attracted a lot of attention recently[1,2]. The application of topological band theory to photonics opens the door to novel devices such as topological lasers[3,4,5,6,7], and stimulates the exploration of new topological phases, such as Floquet[8] and highorder topological insulators[2,9]. We know that most electronic topological systems have their photonic counterparts, except for those depending on the intrinsic properties of fermion system, for example, 2D and 3D topological insulators[29,30] with T 2 1⁄4 À1, where T is the Identifying nodal features in the band structure of topological materials, such as nodal points (Dirac or Weyl points) or nodal lines, can help to understand their topological characters. Among various topological features in momentum space, nodal chain[34,35,36,37,38] is a special configuration of nodal lines[35,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53] where two nodal curves touch at isolated points. Making use of symmetries being intrinsic to electromagnetism, we theoretically propose and experimentally demonstrate a type
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