Magnetic flux penetration in Nb superconducting films with lithographically defined micro-indentations

We present a thorough investigation by magneto-optical imaging of the magnetic flux penetration in Nb thin films with lithographically defined micro-indentations. We demonstrate that discontinuity lines (d-lines) caused by the abrupt bending of current stream lines around the indentations, follow a nearly parabolic shape with concavity depending on the exact form and size of the indentation. We observe a progressive widening of the parabolic d-lines with increasing temperature whose origin may be linked to the weakening of the non-linearity of the current-voltage characteristics. These findings are corroborated and backed up by rigorous numerical simulations and analytical calculations. In addition, we show that the presence of nearby indentations and submicrometer random roughness of the sample border severely modifies the flux front topology. Unlike what has been predicted in the literature, indentations do not serve as nucleation spots for triggering flux avalanches, but instead help to release the flux pressure and avoid magnetothermal instabilities.