Title: Microscopic Theory of Cooper-pair fluctuations in a 2D Electron System with Strong Spin-Orbit Scatterings: Phase Separation and Large Magnetoresistance

Abstract: A microscopic theory of Cooper-pair fluctuations (CPFs) in a 2D electron system with strong spin-orbit scatterings is presented to account for the observation, at low temperatures, of large magnetoresistance (MR) above a crossover field to superconductivity in electron-doped SrTiO$_{3}$/LaAlO$% _{3} $ interfaces. It is found that, while the conventional (diagrammatic) microscopic theory of superconducting fluctuations fails to account for the pronounced MR, an extension of the theory, which introduces a proper definition of the CPFs density, reveals an operative mechanism of this intriguing effect. Phase separation due to Coulomb repulsion, from the rarefying unpaired normal-state electron gas, following field-induced condensation of CPFs in real-space mesoscopic puddles, are in the core of this mechanism. These findings enable us to amend the state-of-the-art microscopic theory, in a consistent manner with the time dependent GL functional approach used previously in an extensive account of the experimentally reported effect.