Effective theory of exotic superconductivity in LaAlO3/SrTiO3 interfaces

Motivated by experimental and theoretical works about superconductivity at the oxide interfaces, we provide a simple model for possible unconventional pairings inside the exotic two-dimensional electron gas formed in heterostructures of SrTiO3 and LaAlO3. At the low energy limit, the electron gas at the interfaces is usually modeled with an effective three band model considering of 3d t2g orbitals which are slightly coupled by atomic spin-orbit couplings (SOC). Considering direct superconducting pairing in two higher delocalized bands and by exploiting a perturbative scheme based on canonical transformation, we derive the effective pairing amplitudes with possibly exotic nature inside the localized dxy band as well as various inter-band pairing components. In particular we show that equal-spin triplet pairings are possible between the band dxy and any of other dxz and dyz bands. In addition weaker effective pairings take place inside the localized band itself and between delocalized dxz and dyz bands with singlet and opposite-spin triplet characters. These unconventional effective pairings are indeed mediated by SOC-induced higher order virtual transitions between the bands and particularly into the localized band. Our model suggest that unconventional effective superconductivity is possible at oxide interfaces, simply, due to the special band structure and important role of atomic SOC and perhaps other magnetic effects present at these heterostructures.