Recently, scanning tunneling microscopy on the Bi-2212 cuprate superconductor has revealed a spatial variation of the energy gap that is directly correlated with a modulation of the apical oxygen position. We identify two mechanisms by which out-of-plane oxygens can modulate the pairing interaction within the CuO2 layer: a covalency between the x2-y2 band and apical p orbital, and a screening of correlation U by apical oxygen polarization. Both effects strongly depend on the apical oxygen position, and their cooperative action explains the experiment.
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