Universal intermediate phases and nanostructures of high-temperature superconductors

The phase diagrams of cuprate superconductors are frequently oversimplified and represented by a cartoon in which T-c(x) is parabolic. It is then supposed, at least in many theories, that a single continuous metal-insulator transition occurs near the optimal composition x = x(c), where T-c is maximized. In fact, the actual phase diagrams are not parabolic, but are described, even in the simplest case (LSCO), better by a trapezoid, with two phase transitions, not one. Because of strong electron-phonon interactions, the two transitions are broadened and obscured by spinodal immiscibility gaps. Examples of such gaps show how they can be identified and related to the formation of nanodomains and filaments.