We present a multiband model for superconductivity at the metallic interface between insulating oxides ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$ (001). Using a self-consistent Bogoliubov–de Gennes theory, formulated with the realistic bands at the interface, we investigate the spin-singlet and spin-triplet pairings in intraband and interband channels. We find that the Rashba and atomic spin-orbit interactions at the interface induce singlet pairing in the interband channel and triplet pairing in both the intraband and interband channels when the pairing amplitude in the singlet intraband channel is finite. The gate-voltage variation of superconductivity is resolved in different pairing channels, compared with experimental results, and found to match quite well. Interestingly, an enhancement of the superconducting transition temperature by external in-plane magnetic field is found, revealing the existence of a hidden superconducting state above the observed one. As the interface is known to possess a high level of inhomogeneity, we explore the role of nonmagnetic disorder incorporating thermal phase fluctuations by using a Monte Carlo method. We show that even after the transition to the nonsuperconducting phase, driven by temperature or magnetic field, the interface possesses localized Cooper pairs whose signature was observed in previous experiments.

• Received 10 July 2015
• Revised 3 October 2015

DOI:https://doi.org/10.1103/PhysRevB.92.174531