Evidence for superconducting vortices in the insulating regime of the LaAlO₃–SrTiO₃ interface electron system

A superconducting phase with an extremely low carrier density of order 10¹³/cm² is present at LaAlO₃–SrTiO₃ interfaces. If depleted from charge carriers by means of a gate field, this superconducting phase undergoes a transition into an insulating state that is, however, characterized by a gap in the spectral density of states. Measuring and analyzing the critical field of this gap, we provide evidence that macroscopically phase-coherent Cooper pairs are present in the insulating state. This state is characterized by fluctuating vortex-antivortex pairs, and not by individual, immobile Cooper pairs.