We study superconducting microtraps with rectangular shapes for cold atomic gases. We present a general argument why microtraps open, if brought close to the surface of the superconductor. We show that for a given width of the strips there exists an
optimal thickness under which the closest distance of the microtrap from the superconductor can be achieved. The distance can be significantly improved, if the edge enhancement of the supercurrent near edges and corners is exploited. We compare numerical calculations with results from conformal mapping and show that conformal mapping can often give useful approximate results.
We study the influence of Born impurity scattering on the zero-energy Andreev bound states near the surface of a d-wave superconductor with and without an externally applied magnetic field. Without an external magnetic field we show that the effect o
f Born impurity scattering is stronger at the surface than in the bulk. In the presence of an external magnetic field the splitting of the zero-energy Andreev bound states is shown to have a nonmonotonous temperature dependence. Born impurity scattering does not wash out the peak splitting, but instead the peak splitting is shown to be quite robust against impurities. We also show that a nonzero gap renormalization appears near the surface.
