Coulomb frustrated phase separation in bilayer electronic systems

We have previously proven that in clean two dimensional electronic systems, long range Coulomb interactions convert what might otherwise have been a first order transition between a high density liquid and a low density insulating electron crystalline phase into a sequence of continuous phase transitions between various sorts of intermediate ``electronic microemulsion phases.'' Here, we consider the electronic micromemulsion phases in a bilayer system, with Coulomb interactions both within and between the layers. At mean-field level, we find infinite families of modulated phases, with a subtle interplay of the period and magnitude of the density oscillations in the two layers.