We have studied the electronic properties of the 2D electron liquid present at the LaAlO$_3$/SrTiO$_3$ interface in series of samples prepared at different growth temperatures. We observe that interfaces fabricated at 650{deg}C exhibit the highest lo
w temperature mobility ($approx 10000 textrm{ cm}^2/textrm{Vs}$) and the lowest sheet carrier density ($approx 5times 10^{12} textrm{ cm}^{-2}$). These samples show metallic behavior and Shubnikov-de Haas oscillations in their magnetoresistance. Samples grown at higher temperatures (800-900{deg}C) display carrier densities in the range of $approx 2-5 times 10^{13} textrm{ cm}^{-2}$ and mobilities of $approx 1000 textrm{ cm}^2/textrm{Vs}$ at 4K. Reducing their carrier density by field effect to $8times 10^{12} textrm{ cm}^{-2}$ lowers their mobilites to $approx 50 textrm{ cm}^2/textrm{Vs}$ bringing the conductance to the weak-localization regime.
Using field effect devices with side gates, we modulate the 2 dimensional electron gas hosted at the LaAlO$_3$/SrTiO$_3$ interface to study the temperature and doping evolution of the magnetotransport. The analysis of the data reveals different trans
port regimes depending on the interplay between the different (elastic, inelastic, and spin-orbit) scattering times and their temperature dependencies. We find that the spin-orbit interaction strongly affects the low temperature transport in the normal state in a very large region of the phase diagram, extending beyond the superconducting dome.
We investigate the 2-dimensional Fermi surface of high-mobility LaAlO$_3$/SrTiO$_3$ interfaces using Shubnikov-de Haas oscillations. Our analysis of the oscillation pattern underscores the key role played by the Rashba spin-orbit interaction brought
about by the breaking of inversion symmetry, as well as the dominant contribution of the heavy $d_{xz}$/$d_{yz}$ orbitals on electrical transport. We furthermore bring into light the complex evolution of the oscillations with the carrier density, which is tuned by the field effect.
