  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.
