  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 the conventional (diagrammatic) microscopic theory
of superconducting fluctuations yields corrections to the normal-state
conductivity too small to account for the pronounced MR. However, an extension
of the theory, which introduces a proper definition of the CPFs density,
reveals an operative mechanism of this intriguing large MR. A crossover to
phase separation, due to Coulomb repulsion, between the rarefying unpaired
normal-state electron gas and condensates of CPFs in real-space mesoscopic
puddles, developed under increasing field, drive a crossover to a large MR. In
the framework of this scenario it is possible to amend the state-of-the-art
microscopic theory consistently with the time dependent Ginzburg-Landau
functional approach, used previously in an extensive account of the
experimentally reported effect.
