Coherence between superconducting edge states in superconducting periodic arrays of artificial defects

The transition line of superconducting arrays of holes exhibits a rich field structure due to the interference of superconducting states nucleated at the holes edges. We studied by means of resistance measurements their effect on the T*c(H) line as a function of transverse magnetic field using regular arrays of nanofabricated micron size holes. The arrays transition fields are higher than for the bulk. Moreover we found a nontrivial field modulation of the T*c(H) line with an inversion, with increasing field, of the modulation concavity which we assigned to a crossover from a collective to an isolated edge state regime. The high field regime is well described by the nucleation at a single hole in an infinite film. The modulation at low fields was found to be dominated by the interference of neighbor edge states when the inter-hole distance w becomes comparable to the temperature dependent coherence length. A comparison between arrays of different hole shape shows the influence of geometry on the type of interaction established, which can described either as a superconducting wire network or as a weak link array.