Phase separation and long-wavelength charge instabilities in spin-orbit coupled systems

We investigate a two-dimensional electron model with Rashba spin-orbit interaction where the coupling constant g = g( n) depends on the electronic density. It is shown that this dependence may drive the system unstable towards a long-wavelength charge density wave (CDW) where the associated second-order instability occurs in close vicinity to global phase separation. For very low electron densities the CDW instability is nesting- induced and the modulation follows the Fermi momentum k(F). At higher density the instability criterion becomes independent of k(F) and the system may become unstable in a broad momentum range. Finally, upon filling the upper spin- orbit split band, finite momentum instabilities disappear in favor of phase separation alone. We discuss our results with regard to the inhomogeneous phases observed at the LaAlO3/SrTiO3 or LaTiO3/SrTiO3 interfaces. Copyright (C) EPLA, 2015