Dominance of spin-orbit coupling in magnetotransport at the LaAlO$_3$/SrTiO$_3$ interface

Today, the planar confinement of electrons is no longer synonymous with semiconducting quantum wells. The mobile electrons at the metallic LAO/STO interface are better confined by at least one order of magnitude, in a regime closer to that achieved in graphene. Nonetheless, graphene and, for example, GaAs/AlGaAs quantum well have more in common with each other than with LAO/STO. In these two systems, spin-orbit coupling effects are for many purposes unimportant or negligibly weak, and neither system has ever shown superconductivity. In contrast, spin-orbit coupling effects are strong at the LAO/STO interface, and superconductivity is a well established, potentially quite exotic, feature. We measure the resistance of the LAO/STO interface in an in-plane magnetic field perpendicular to the current, for a wide range of applied fields B, temperatures, and carrier densities controlled by a back-gate voltage $V_g$. Our measurements show dramatic, fast and very large drops in magnetoresistance, either as a function of B or $V_g$, decrease slowly with temperature and seem suggestive of magnetic ordering. However, they compare very well with an alternative explanation that strongly suggests that the effect of spin-orbit coupling on the band structure alone can dominate magnetotransport.