Role of edge superconducting states in trapping of multi-quanta vortices by microholes. Application of the bitter decoration technique

Abstract

The Bitter decoration technique is used to study the trapping of single and multiple quanta vortices by a lattice of circular microholes. By keeping a thin superconducting layer (the bottom) inside each hole we are able to visualise the trapped vortices. From this we determine, for the first time, the filling factor FF, i.e. the number of vortices captured inside a hole. In all cases the sample is cooled at a constant field before making the decoration. Two qualitatively different states of the vortex crystal are observed: (i) In case when the interhole distance is much larger than the coherence length, the filling factor averaged over many identical holes (〈(FF〉)) is a stepwise function of the magnetic flux (of the external field) through the hole, because each hole captures the same number of vortices. The density of fluxoids inside the openings is higher than in the uniform film, but much lower than it should be in the state of equilibrium. We claim that the number of trapped vortices is determined by the edge superconducting states which appear around each hole at the modified third critical fieldH _c3 ^* >H _c2 . BelowH _c2 such states produce a surface barrier of a new type. This barrier for the vortex entrance and exit is due to the strong increase of the order parameter near the hole edge. It keeps constant the number of captured vortices during the cooling at a fixed field, (ii) An increase of the hole density or of the hole radius initiates a sharp redistribution of fluxoids: all of them drop inside holes. This first order transition leads to a localization of all vortices and consequently to a qualitative change of the transport properties (TAFF in our case). In the resulting new state the filling factor is not any more the same for neighbouring holes and its averaged value is equal to the frustration of the hole network.