Scanning SQUID measurements of the superconducting state of $\delta$-doped SrTiO$_3$ heterostructures

The discovery of interface superconductivity in complex oxide heterostructures has generated significant excitement. We used scanning SQUID microscopy to investigate the magnetic properties of one such heterostructure, $\delta$-doped structures in SrTiO$_3$ thin films. We have observed a diamagnetic response and imaged vortices providing further evidence of a two-dimensional superconducting state. Finally we measured the magnetic susceptibility from which we observe spatial inhomogeneities in the superconducting response and can estimate the temperature dependence of the magnetic penetration depth.