Recently superconductivity at the interface between the insulators LaAlO3 and SrTiO3 has been tuned with the electric field effect to an unprecedented range of transition temperatures. Here we perform a detailed finite size scaling analysis to explore the compatibility of the phase transition line with Berezinskii-Kosterlitz-Thouless (BKT) behavior and a 2D-quantum phase(QP)-transition. In an intermediate regime, limited by a gate voltage dependent limiting length, we uncover remarkable consistency with a BKT-critical line ending at a metallic quantum critical point, separating a weakly localized insulator from the superconducting phase. Our estimates for the critical exponents of the 2D-QP-transition, z=1 and nu=0.66, suggest that it belongs to the 3D-xy universality class.
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