Topologically Charged Nodal Surface

We report the existence of topologically charged nodal surface, a band degeneracy on a two-dimensional surface in momentum space that is topologically charged. We develop a Hamiltonian for such charged nodal surface, and show that such a Hamiltonian can be implemented in a tight-binding model as well as in an acoustic meta-material. We also identify a topological phase transition, through which the charges of the nodal surface changes by absorbing or emitting an integer number of Weyl points. Our result indicates that in the band theory, topologically charged objects are not restrict to zero dimension as in a Weyl point, and thus pointing to previously unexplored opportunities for the design of topological materials.