Friedel Oscillations and superconducting-gap enhancement by impurity scattering
Experiments observe an enhanced superconducting gap over impurities as compared to the clean-bulk value. In order to shed more light on this phenomenon, we perform simulations within the framework of Bogoliubov-deGennes theory applied to the attractive Hubbard model. The simulations qualitatively reproduce the experimentally observed enhancement effect; it can be traced back to an increased particle density in the metal close to the impurity site. In addition, the simulations display significant differences between a thin (2D) and a very thick (3D) film. In 2D pronounced Friedel oscillations can be observed, which decay much faster in (3D) and therefore are more difficult to resolve. Also this feature is in qualitative agreement with the experiment.