Response of fractal penetration of magnetic flux to disorder landscape in superconducting films

Magnetic flux front and induction contours in superconducting YBa2Cu3O7-d films with defect size s ~ l (superconducting coherence length) and s > l are studied by magneto-optical imaging. Robust self-affine spatial correlation was observed using scaling analysis in the small pinning-dominated (s ~ l) disorderd films. The roughness exponent was determined to be ~ 0.66, independent of numbers of defects (or the film thickness). When the disorder landscape also included a distribution of large defects (s >> l), the flux front and induction contours exhibited self-similarity, with a fractal dimension to be ~ 1.33 using the box-counting method. The remarkably different flux penetration patterns were shown to be the manifestation of self-organized criticality at different length scales.