# Experimental discovery of nodal chains

## TL;DR

This paper reports the theoretical prediction and experimental observation of nodal chains in a photonic crystal, overcoming previous material limitations and revealing new topological line-degeneracy phenomena with potential for advanced wave dynamics.

## Contribution

It introduces the first experimental realization of nodal chains in a metallic-mesh photonic crystal, demonstrating their protected topological features and complex surface states.

## Key findings

- Nodal chains are frequency-isolated and protected by mirror symmetries.
- Angle-resolved transmission and Fourier-transformed field scan reveal bulk and surface dispersions.
- Nodal chains exhibit quadratic surface band touchings, enriching topological wave dynamics.

## Abstract

Three-dimensional (3D) topological nodal points, such as Weyl and Dirac nodes have attracted wide-spread interest across multiple disciplines and diverse material systems. Unlike nodal points that contain little structural variations, nodal lines can have numerous topological configurations in the momentum space, forming nodal rings, nodal chains and potentially nodal links and nodal knots. However, nodal lines have much less development for the lack of ideal material platforms. In condensed matter for example, nodal lines are often fragile to spin-orbit-coupling, locating off the Fermi level, coexisting with energy-degenerate trivial bands and dispersing strongly in energy of the line degeneracy. Here, overcoming all above difficulties, we theoretically predict and experimentally observe nodal chains in a metallic-mesh photonic crystal having frequency-isolated linear bandtouching rings chained across the entire Brillouin zone (BZ). These nodal chains are protected by mirror symmetries and have a frequency variation less than 1%. We used angle-resolved transmission (ART) to probe the projected bulk dispersions and performed Fourier-transformed field scan (FTFS) to map out the surface dispersions, which is a quadratic touching between two drumhead surface bands. Our results established an ideal nodal-line material for further studies of topological line-degeneracies with nontrivial connectivities, as well as the consequent wave dynamics richer than 2D Dirac and 3D Weyl materials.