Universal Aspects of Coulomb-Frustrated Phase Separation

We study the consequences of Coulomb interactions on a system undergoing a putative first order phase transition. In two dimensions (2D), near the critical density, the system is universally unstable to the formation of new intermediate phases, which we call "electronic microemulsion phases," which consist of an intermediate scale mixture of regions of the two competing phases. A corollary is that there can be no direct transition as a function of density from a 2D Wigner crystal to a uniform electron liquid. In 3D, if the strength of the Coulomb interactions exceeds a critical value, no phase separation occurs, while for the weaker Coulomb strength electronic microemulsions are inevitable. This tendency is considerably more pronounced in anisotropic (quasi-2D or quasi-1D) systems, where a devil's staircase of transitions is possible.