Pairing modulations and phase separation instabilities in Bi2Sr2CaCu2O8 + δ

There is growing evidence that the unconventional spatial inhomogeneities in the doped high-Tc superconductors are accompanied by the pairing of electrons, subsequent phase transitions and condensation into coherent states. We show that such pairing states can be obtained from phase separation instabilities near level crossings. Conditions for coherent pairing instabilities are examined using exact diagonalization of Hubbard-like pyramid structures under variation of coupling and interaction strengths. We also evaluate the behavior of the energy charge gap in the vicinity of level crossings using a parametrization of coupling to the apical site to represent out-of-plane effects. These results provide a simple microscopic explanation of (correlation induced) supermodulation of the coherent pairing gap observed in scanning tunneling microscopy measurements at atomic scale in Bi2Sr2CaCu2O8 + δ.