The Effects of Phase Separation in the Cuprate Superconductors

TL;DR

This paper models phase separation in cuprate superconductors using the Cahn-Hilliard equation, linking it to pseudogap phenomena and charge inhomogeneity, and providing quantitative agreement with experimental patterns.

Contribution

It introduces a quantitative phase separation model for cuprates using Cahn-Hilliard and Ginzburg-Landau formalisms, connecting charge segregation to pseudogap behavior.

Findings

Charge segregation into two hole density states is quantitatively modeled.

The energy barrier between densities explains the upper pseudogap.

Simulation reproduces observed stripe and granular patterns.

Abstract

Phase separation has been observed by several different experiments and it is believed to be closely related with the physics of cuprates but its exactly role is not yet well known. We propose that the onset of 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 %on the hole doping and temperature %dependence of the degree of the charge inhomogeneity in agreement with %some experiments and the simulations reproduce the observed stripe and granular pattern of segregation. Furthermore, with a Bogoliubov-deGennes (BdG) local superconducting critical temperature calculation for the lower pseudogap or the onset of local superconductivity, it yields novel interpretation of several non-conventional measurements on cuprates.