A theory for superconductor-to-insulator transitions in a 2D electron liquid with strong spin-orbit impurity scattering

Superconductor-to-insulator transition (SIT) in 2D electron systems is an intriguing, controversial phenomenon in condensed matter physics, with no consensus as to its fundamental mechanism and expected ramifications. Here we develop a theory of SIT in a 2D electron system, based solely on the opposing effects generated by Cooper-pair fluctuations: The large enhancement of conductivity due to fluctuating Cooper pairs (para-conductivity) in approaching the critical magnetic field, and its suppression associated with the loss of unpaired electrons due to Cooper-pairs formation. The theory is tested using a model of a 2D electron liquid under a strong magnetic field subject to Zeeman spin-splitting pair-breaking and strong spin-orbit impurity scattering, which is realized experimentally in the system of electrons created in the (111) interface between crystalline SrTiO_{3} and LaAlO_{3}. Employing a modified Ginzburg-Landau (GL) functional approach, in which the interaction between Gaussian fluctuations are treated within the self-consistent Hartree approximation, the calculated sheet resistivity accounts well for extensive magnetoresistance (MR) data reported recently for the above mentioned 2D electron system. At low temperatures, where the calculated MR curves exhibit quick narrowing of the MR peak versus the measured data, which show remarkable saturation upon decreasing temperature, the effect of quantum tunneling of cooper-pair through GL energy barriers is introduced within a phenomenological approach, yielding very good quantitative agreement with the experiment in the entire temperatures range.