Screened superexchange mechanism for superconductivity applied to cuprates

In 1965, Kohn and Luttinger published a note revealing that dynamical screening of the repulsive Coulomb interaction leads, under certain conditions, to an effective attraction necessary for the formation of Cooper pairs. We propose such a formalism adapted to the cuprates, where the screening arises from the superexchange dynamics of virtual holes in the oxygen orbitals of the CuO2 plane. Using an adequate Schrieffer–Wolff transformation, the basic Hartree–Fock–Bogoliubov method, and the ab initio data on orbitals (energy, hopping, interaction), we derive some predictions for the temperature-doping phase diagram (pseudo-gap, strange metal, antiferromagnetism, superconducting, and normal states) and for the doping-dependent band energy spectrum in semi-quantitative agreement with observations.