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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. 

Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize fragile Bloch bands that challenge our very notion of topology: Although answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial Bloch bands. Here, we fully characterize the symmetry properties of the response of an acoustic metamaterial to establish the fragile nature of the low-lying Bloch bands. Additionally, we present a spectral signature in the form of spectral flow under twisted boundary conditions.