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We investigate a two-dimensional electron model with Rashba spin-orbitinteraction where the coupling constant $g=g(n)$ depends on the electronicdensity. It is shown that this dependence may drive the system unstable towardsa long-wave length charge density wave (CDW) where the associated second orderinstability occurs in close vicinity to global phase separation. For very lowelectron densities the CDW instability is nesting-induced and the modulationfollows the Fermi momentum $k_F$. At higher density the instability criterionbecomes independent of $k_F$ and the system may become unstable in a broadmomentum range. Finally, upon filling the upper spin-orbit split band, finitemomentum instabilities disappear in favor of phase separation alone. We discussour results with regard to the inhomogeneous phases observed at theLaAlO$_3$/SrTiO$_3$ or LaTiO$_3$/SrTiO$_3$ interfaces.

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