We explore the superconducting phase diagram of the two-dimensional electron system at the LaAlO3/SrTiO3 interface by monitoring the frequencies of the cavity modes of a coplanar waveguide resonator fabricated in the interface itself. We determine the phase diagram of the superconducting transition as a function of the temperature and electrostatic gating, finding that both the superfluid density and the transition temperature follow a dome shape but that the two are not monotonically related. The ground state of this two-dimensional electron system is interpreted as a Josephson junction array, where a transition from long- to short-range order occurs as a function of the electronic doping. The synergy between correlated oxides and superconducting circuits is revealed to be a promising route to investigate these exotic compounds, complementary to standard magnetotransport measurements.

Quantum confinement at complex oxide interfaces establishes an intricate hierarchy of the strongly correlated d orbitals which is widely recognized as a source of emergent physics. The most prominent example is the (001) LaAlO3/SrTiO3 (LAO/STO) interface, which features a dome-shaped phase diagram of superconducting critical temperature and spin-orbit coupling (SOC) as a function of electrostatic doping, arising from a selective occupancy of t2g orbitals of different character. Here we study (111)-oriented LAO/STO interfaces, where the three t2g orbitals contribute equally to the subband states caused by confinement, and investigate the impact of this unique feature on electronic transport. We show that transport occurs through two sets of electronlike subbands, and the carrier density of one of the sets shows a nonmonotonic dependence on the sample conductance. Using tight-binding modeling, we demonstrate that this behavior stems from a band inversion driven by on-site Coulomb interactions. The balanced contribution of all t2g orbitals to electronic transport is shown to result in strong SOC with reduced electrostatic modulation.