Large modulation of the Shubnikov-de Haas oscillations by the Rashba interaction at the LaAlO${}_3$/SrTiO${}_3$ interface

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.