Charge modulation at the surface of high-Tc 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.