Effects of phase separation in the cuprate superconductors

Phase separation has been observed by several different experiments and it is believed to be closely related with the physics of cuprates but its exact role is not yet well known. We propose that the onset of the pseudogap phenomenon or the upper pseudogap temperature T* has its origin in a spontaneous phase separation transition at the temperature T-ps=T*. In order to perform quantitative calculations, we use a Cahn-Hilliard (CH) differential equation originally proposed to the studies of alloys and on a spinodal decomposition mechanism. Solving numerically the CH equation it is possible to follow the time evolution of a coarse-grained order parameter which satisfies a Ginzburg-Landau free-energy functional commonly used to model superconductors. In this approach, we follow the process of charge segregation into two main equilibrium hole density branches and the energy gap normally attributed to the upper pseudogap arises as the free-energy potential barrier between these two equilibrium densities below T-ps. This simulation provides quantitative results in agreement with the observed stripe and granular pattern of segregation. Furthermore, with a Bogoliubov-deGennes local superconducting critical temperature calculation for the lower pseudogap or the onset of local superconductivity, it yields an interpretation of several nonconventional measurements on cuprates.