  The two-dimensional electron gas at the LaTiO3/SrTiO3 or LaAlO3/SrTiO3 oxide
interfaces becomes superconducting when the carrier density is tuned by gating.
The measured resistance and superfluid density reveal an inhomogeneous
superconductivity resulting from percolation of filamentary structures of
superconducting "puddles" with randomly distributed critical temperatures,
embedded in a non-superconducting matrix. Following the evidence that
superconductivity is related to the appearance of high-mobility carriers, we
model intra-puddle superconductivity by a multi-band system within a weak
coupling BCS scheme. The microscopic parameters, extracted by fitting the
transport data with a percolative model, yield a consistent description of the
dependence of the average intra-puddle critical temperature and superfluid
density on the carrier density.
