Frustrated phase separation in two-dimensional charged systems

We study phase-separation frustrated (FPS) by the long-range Coulomb interaction in two-dimensional electronic systems with emphasis to the case of a metallic and an insulating phase. In the mixed phase, the system self-organizes in terms of mesoscopic inhomogeneities of one phase hosted by the other phase. We analyze the cases of circular drops and alternating stripes. As a first approximation, we consider the density inside each inhomogeneity as constant and in some cases, we test the accuracy of this assumption by a more involved local density approximation. We find that the transition from the uniform phase to the frustrated phase-separated phase changes order depending upon its geometric arrangement. Contrary to what was found in three-dimensional systems, there is no upper bound for the size of inhomogeneities. This difference stands on the different role of the long-range Coulomb interaction and screening in two- and three-dimensional systems. We conclude that two-dimensional systems are more prone to mesoscopic FPS.