The two-dimensional electron gas at the crystalline ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ ($c$-LAO/STO) interface has sparked large interest due to its exotic properties, including an intriguing gate-tunable superconducting phase. While there is growing evidence of pronounced spatial inhomogeneity in the conductivity at STO-based interfaces, the consequences for superconductivity remain largely unknown. We study interfaces based on amorphous LAO top layers grown at room temperature ($a$-LAO/STO) and demonstrate a superconducting phase similar to $c$-LAO/STO, however, with a gate-tunable critical temperature of $460\mathrm{mK}$. The dependence of the superconducting critical current on temperature, magnetic field, and back-gate-controlled doping is found to be consistently described by a model of a random array of Josephson-coupled superconducting domains.

• Received 1 October 2015
• Revised 27 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.184504