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

The transition line of superconducting arrays of holes exhibits a rich fiel d structure due to the interference of superconducting states nucleated at the holes edges. We studied by means of resistance measurements their effec t on the T-c*(H) line as a function of transverse magnetic field using regu lar arrays of nanofabricated micron size holes, The arrays transition field s are higher than for the bulk, Moreover we found a nontrivial field modula tion of the T-c*(H) line with an inversion, with increasing field, of the m odulation concavity which we assigned to a crossover from a collective to a n isolated edge state regime. The high field regime is well described by th e nucleation at a single hole in an infinite film. The modulation at low fi elds was found to be dominated by the interference of neighbor edge states when the inter-hole distance w becomes comparable to the coherence length x i(T-c*). A comparison between arrays of different hole shape shows the infl uence of geometry on the type of interaction established, which can describ ed either as a superconducting wire network or as a weak link array.