We develop a model for high-Tc superconductors based on an electronic phase separation where low-and high-density domains are formed. At low temperatures this system may act as a granular superconductor forming an array of Josephson junctions. Cuprat
es are also known to have low superfluid densities and strong correlation effects. Both characteristics activate a negative Josephson coupling due to frustration that leads to spontaneous currents responsible for the weak ferromagnetic order. This original approach reproduces the observed onset of spontaneous magnetic signal and its dependence on the doping level.
The segregation of oxygen in the high critical temperature cuprate superconductor $La_2CuO_{4+y}$ has been systematically studied along the years. In a recent set of experiments, Poccia et al related, for the first time, time ordering ($t$) of oxygen
interstitials with the corresponding superconducting transition temperature $T_c(t)$. We develop a phenomenological description of the time ordering forming pattern domains and show how it may affect the superconducting interaction. The superconducting self-consistent calculations in a system with electronic granular structure of varying hole doping yields also different local d-wave amplitudes. These amplitudes are of the order of magnitude of scanning tunneling microscopy measurements and they vanish at $T^*(t)> T_c(t)$. Then, calculations with Josephson coupling among the isolated charge domains reveal that the superconducting interaction is likely to be scaled by the local free energy and capture the details of $T_c(t)$. The accurately reproduction of these apparently disconnected phenomena establishes routes to the important physical mechanisms involved in the connection between sample production and on the origin of the superconductivity of cuprates.
The appearance of the Fermi arcs or gapless regions at the nodes of the Fermi surface just above the critical temperature is described through self-consistent calculations in an electronic disordered medium. We develop a model for cuprate superconduc
tors based on an array of Josephson junctions formed by grains of inhomogeneous electronic density derived from a phase separation transition. This approach provides physical insights to the most important properties of these materials like the pseudogap phase as forming by the onset of local (intragrain) superconducting amplitudes and the zero resistivity critical temperature $T_c$ due to phase coherence activated by Josephson coupling. The formation of the Fermi arcs and the dichotomy in k-space follows from the direction dependence of the junctions tunneling current on the d-wave symmetry on the $CuO_2$ planes. We show that this semi-phenomenological approach reproduces also the main future of the cuprates phase diagram.
There are processes in nature that resemble a true force but arise due to the minimization of the local energy. The most well-known case is the exchange interaction that leads to magnetic order in some materials. We discovered a new similar process o
ccurring in connection with an electronic phase separation transition that leads to charge inhomogeneity in cuprate superconductors. The minimization of the local free energy, described here by the Cahn-Hilliard diffusion equation, drives the charges into regions of low and high densities. This motion leads to an effective potential with two-fold effect: creation of tiny isolated regions or micrograins, and two-body attraction, which promotes local or intra-grain superconducting pairing. Consequently, as in granular superconductors, the superconducting transition appears in two steps. First, with local intra-grain superconducting amplitudes and, at lower temperature, the superconducting phase or resistivity transition is attained by intergrain Josephson coupling. We show here that this approach reproduces the main features of the cuprates phase diagram, gives a clear interpretation to the pseudogap phase and yields the position dependent local density of states gap $Delta(vec r)$ measured by tunnelling experiments.
The resistivity as function of temperature of high temperature superconductors is very unusual and despite its importance lacks an unified theoretical explanation. It is linear with the temperature for overdoped compounds but it falls more quickly as
the doping level decreases, and for weakly doped samples it has a minimum, increases like an insulator before it drops to zero at low temperatures. We show that this overall behavior can be explained by calculations using an electronic phase segregation into two main component phases with low and high densities. The total resistivity is calculated by the various contributions through several random picking processes of the local resistivities and using the Random Resistor Network approach.
