Observation of non-Abelian nodal links in photonics

TL;DR

This paper reports the experimental observation of non-Abelian nodal links in a photonic metamaterial, revealing complex topological structures and surface states, advancing understanding of non-Abelian topological charges in momentum space.

Contribution

First experimental demonstration of non-Abelian nodal links in photonics using a biaxial hyperbolic metamaterial, illustrating complex topological configurations and associated surface states.

Findings

Observation of linked nodal lines formed by three bands

Detection of surface bound states in the continuum (BICs)

Analysis of non-Abelian topological charges and configurations

Abstract

In crystals, two bands may cross each other and form degeneracies along a closed loop in the three-dimensional momentum space, which is called nodal line. Nodal line degeneracy can be designed to exhibit various configurations such as nodal rings, chains, links and knots. Very recently, non-Abelian band topology was proposed in nodal link systems, where the nodal lines formed by consecutive pairs of bands exhibit interesting braiding structures and the underlying topological charges are described by quaternions. Here, we experimentally demonstrate non-Abelian nodal links in a biaxial hyperbolic metamaterial. The linked nodal lines threading through each other are formed by the crossings between three adjacent bands. Based on the non-Abelian charges, we further analyze various admissible nodal link configurations for the three-band system. On the interface between the metamaterial and air, surface bound states in the continuum (BICs) are observed, which serves as the symmetry-enforced derivative of drumhead surface states from the linked nodal lines. Our work serves as a direct observation of the global topological structures of nodal links, and provides a platform for studying non-Abelian topological charge in the momentum space.