Origin of spatial variation of pairing gap in Bi-based high-Tc cuprates

Recently, scanning tunneling microscopy on 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 CuO_2 layer: a covalency between the x^2-y^2 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.