Charge Modulation at the Surface of High-T_c Superconductors

It is shown here that surfaces of high-temperature superconductors are covered by dipole layers. The charge density modulation is induced by the local suppression of the gap function at the surface. This effect is studied in the framework of the Ginzburg-Landau theory and crucially depends on the appropriate boundary conditions. Those are derived from Gor'kov's equations for a d-wave pairing symmetry. Within this framework the structure of the surface dipole layer is determined. The contribution of this charging to a lens-effect of superconducting films with holes, which has been studied in recent experiments, is discussed.