Maximum size of self-organized inhomogeneities in electronic systems

We analyze phase separation among two electronic phases, frustrated by the long-range Coulomb interaction in the presence of a rigid background. The system self-organizes in islands of one phase hosted by the other phase. The size of the islands is determined by minimizing a free energy that takes into account both surface energy and Coulomb effects. We report the results in three dimensions, in particular the size of the islands has an upper bound given by a scale of the order of the electric field screening length