Antiferromagnetic exchange mechanism of superconductivity in cuprates

The theory of superconducting pairing due to antiferromagnetic exchange is considered. The strong dependence of the superconducting transition temperature $T_c$ on the lattice constant $a$ observed recently in mercury superconductors is explained within the framework of this theory. Calculations have been performed based on the two-band $p-d$ Hubbard model in the strong correlation limit. The large excitation energy $\Delta_{pd}$ for the antiferromagnetic exchange of two particles from different Hubbard subbands results in the suppression of the retardation effects and in the pairing of all the particles in the conduction subband with the Fermi energy $E_F \ll \Delta_{pd}$: $\, T_c \simeq E_F {\rm exp}{(-1/\lambda)}$, where $\lambda \propto J\,$. The dependence $T_c(a)$ and the isotope effect are explained by the dependence of the exchange interaction $J$ on $a$ and on zero-point vibrations of oxygen ions.