Signatures of local superconducting islands at elevated temperatures in LaAlO$_3$/SrTiO$_3$ Heterostructure Interface

Superconductivity has been observed in LaAlO$_3$ /SrTiO$_3$ heterostructures below 300 mK in resistivity measurements and later confirmed with Meissner effect. Our detailed magnetization measurements in several LaAlO$_3$/SrTiO$_3$ samples indicate a quasi superconducting state persisting up to 4 K. In these samples, we discovered large nonreversible magnetization vs. field curves. Moreover, the magnitude of the nonreversible loop is proportional to sweep rates, suggesting that it is caused by local magnetic moments generated by eddy currents. Based on this eddy current picture, the inferred conductance is found to be 7 orders of magnitude larger than the conductance across the whole interface. This contrast suggests the existence of small local quasi superconducting regions at a temperature of 4 K, well above the long range superconducting transition temperature.