Magnetotransport of a 2DEG with anisotropic Rashba interaction at the LaAlO$_3$/SrTiO$_3$ interface

We investigate the magnetotransport properties of a two-dimensional electron gas with anisotropic k-cubic Rashba interaction at the $\rm{LaAlO_3}$/$\rm{SrTiO_3}$ interface. The Landau levels and density of states of the system as well as the magnetotransport coefficients are evaluated. A somehow anomalous beating pattern in low magnetic field regime is found both in the density profile and magnetoresistivity. We discuss the impact of electron density, Landau level broadening and Rashba spin-orbit constant on the appearance of the beatings in low magnetic fields and find that at low electron concentrations and not very strong spin-orbit interactions the beatings smooth out. On the other hand, as the magnetic field increases, the Zeeman term becomes the dominant splitting mechanism leading to the spin-split peaks in SdH oscillations. We also show that the observation of the beatings in low magnetic fields needs a system with rather higher carrier concentration so that the beatings persist up to sufficiently large fields where the oscillations are not smoothed out by Landau level broadening. The quantum Hall plateaus are evaluated and we show the Chern number with both even and odd values is replaced by the odd numbers when two subband energies are close with spin degenerate energy levels. Along with the numerical evaluation of the magnetotransport properties, a perturbative calculation is also performed which can be used in the case of low densities and not very large filling factors.