Experimental demonstration of acoustic semimetal with topologically charged nodal surface

Weyl points are zero-dimensional band degeneracy in three-dimensional momentum space that has nonzero topological charges. The presence of the topological charges protects the degeneracy points against perturbations and enables a variety of fascinating phenomena. It is so far unclear whether such charged objects can occur in higher dimensions. Here, we introduce the concept of charged nodal surface, a two-dimensional band degeneracy surface in momentum space that is topologically charged. We provide an effective Hamiltonian for this charged nodal surface and show that such a Hamiltonian can be implemented in a tight-binding model. This is followed by an experimental realization in a phononic crystal. The measured topologically protected surface arc state of such an acoustic semimetal reproduces excellently the full-wave simulations. Creating high-dimensional charged geometric objects in momentum space promises a broad range of unexplored topological physics.