Electrostatically-tuned superconductor-metal-insulator quantum transition at theLaAlO3/SrTiO3interface

Recently superconductivity at the interface between the insulators ${\text{LaAlO}}_{3}$ and ${\text{SrTiO}}_{3}$ 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 two-dimensional\char21{}quantum-phase (2D-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, $z\ensuremath{\simeq}1$ and $\overline{\ensuremath{\nu}}\ensuremath{\simeq}2/3$, suggest that it belongs to the three-dimensional-$xy$ universality class.