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The appearance of the Fermi arcs or gapless regions at the nodes of the Fermisurface just above the critical temperature is described throughself-consistent calculations in an electronic disordered medium. We develop amodel for cuprate superconductors based on an array of Josephson junctionsformed by grains of inhomogeneous electronic density derived from a phaseseparation transition. This approach provides physical insights to the mostimportant properties of these materials like the pseudogap phase as forming bythe onset of local (intragrain) superconducting amplitudes and the zeroresistivity critical temperature $T_c$ due to phase coherence activated byJosephson coupling. The formation of the Fermi arcs and the dichotomy ink-space follows from the direction dependence of the junctions tunnelingcurrent on the d-wave symmetry on the $CuO_2$ planes. We show that thissemi-phenomenological approach reproduces also the main future of the cupratesphase diagram.

Theory of the Fermi Arcs, the Pseudogap, $T_c$ and the Anisotropy in k-space of Cuprate Superconductors