Dynamical-charge neutrality at a crystal surface

For both molecules and periodic solids, ionic dynamical charge tensors-measuring the coupling of electric fields to ionic displacements-are known to obey a dynamical neutrality condition. This condition forces their sum to vanish over the whole finite system, or over the crystal cell, respectively. We extend this sum rule to the nontrivial case of the surface of a semi-infinite solid and show that, in the case of a polar surface of an insulator, the surface ions cannot have the same dynamical charges as in the bulk. The sum rule is demonstrated through calculations for a couple of SiC surfaces.