Multi-band, two-dimensional superconductivity above the Pauli limit in Sr_1-xNd_xTiO₃

We present evidence of two-dimensional, multi- band superconductivity in Sr_1-xNd_xTiO₃ thin films from the temperature dependence of the resistive upper critical field. The out-of-plane upper critical field shows pronounced positive curvature, which extends substantially below the critical temperature, and further exhibits a change in curvature at low temperatures. Quite unusually, the out-of-plane upper critical field exceeds the Pauli paramagnetic limit, by almost a factor of two. We attribute this unusual observation to the enhancement of critical field due to two-band superconductivity and the presence of strong spin-orbit coupling. We propose a model for the critical field of a two-band superconductor that includes paramagnetic breaking of Copper pairs and spin-orbital coupling in the dirty limit and find good agreement of this model with our data. Our results suggest that in SrTiO₃ intra-band superconducting coupling dominates over inter-band coupling.