Superconductivity and magnetism in a three-band model of the LAO/STO interface from a weak-coupling perspective

Recent experiments on LAO/STO interfaces have shown the occurrence of both superconductivity and magnetism in this system. Motivated by these experiments, we analyze various Fermi-liquid instabilities in a three-band model of the LAO/STO interface with purely repulsive interactions by calculating susceptibilities for superconducting, magnetic and nematic orders. In light of recent transport experiments proposing a Lifshitz transition between d orbitals, we particularly study how the susceptibilities depend on the chemical potential. Further, we investigate the interplay of these different orders.