Central peak position in magnetization loops of high-$T_c$   superconductors
  Exact analytical results are obtained for the magnetization of a superconducting thin strip with a general behavior J_c(B) of the critical current density. We show that within the critical-state model the magnetization as function of applied field, B_a, has an extremum located exactly at B_a=0. This result is in excellent agreement with presented experimental data for a YBCO thin film. After introducing granularity by patterning the film, the central peak becomes shifted to positive fields on the descending field branch of the loop. Our results show that a positive peak position is a definite signature of granularity in superconductors. 
D.V. Shantsev, M. R. Koblischka, Y. M. Galperin, T. H. Johansen, P.   Nalevka, and M. Jirsa