  A superconducting phase with an extremely low carrier density of the order of
10^13 cm^-2 is present at LaAlO3-SrTiO3 interfaces. If depleted from charge
carriers by means of a gate field, this superconducting phase undergoes a
transition into a metallic/insulating state that is still 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 metallic/insulating state. This is
characterized by fluctuating vortex-antivortex pairs, and not by individual,
immobile Cooper pairs. The measurements furthermore yield the carrier-density
dependence of the superconducting coherence length of the two-dimensional
system.
