Observation of signatures of subresolution defects in two-dimensional superconductors with a scanning SQUID

The diamagnetic susceptibility of a superconductor is directly related to its superfluid density. Mutual inductance is a highly sensitive method for characterizing thin films, however, in traditional mutual inductance measurements, the measured response is a nontrivial average over the area of the mutual inductance coils, which are typically of millimeter size. Here we measure localized, isolated features in the diamagnetic susceptibility of Nb superconducting thin films with lithographically defined through holes, $\ensuremath{\delta}$-doped ${\mathrm{SrTiO}}_{3}$, and the two-dimensional electron system at the interface between ${\mathrm{LaAlO}}_{3}$ and ${\mathrm{SrTiO}}_{3}$, using scanning superconducting quantum interference device susceptometry, with spatial resolution as fine as $0.7\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$. We show that these features can be modeled as locally suppressed superfluid density, with a single parameter that characterizes the strength of each feature. This method provides a systematic means of finding and quantifying submicron defects in two-dimensional superconductors.