Airy pattern, weak-link modeling of critical currents in high-Tc superconductors

Abstract

We have measured the transport critical current density at very low magnetic fields in samples of superconducting bulk sintered Y 1 Ba 2 Cu 3 O x , Y 1 Ba 2 Cu 4 O x obtained from several sources. The results are analyzed at low fields (≤10 mT) with a statistical model which assumes that the current is limited by Josephson weak links (SNS or SIS Josephson junctions or microbridges) whose locations are to be determined. Each weak link is assumed to be described by an Airy current-field pattern rather than a Fraunhofer pattern. The former has a better theoretical foundation and is in better agreement with the data, varying as H -3 2 upon averaging. The fitting procedure yields the average cross sectional area of the weak links. By assuming the link thickness to be twice the London penetration depth at 77 K, we find that the average linear dimensions of the links are in all cases comparable to the grain dimensions. The quantitative analysis also confirms the percolation concept, in which a subset of weakest links controls the transport current.