Dependence of the critical temperature of high-temperature cuprate superconductors on hoppings and spin correlations between CuO2 planes

The influence of interlayer hoppings on the superconducting transition temperature (Tc) in bilayer cuprates has been studied. The parameter of hopping between layers is expressed as t⊥(k) = t⊥(cos(kx) − cos(ky))2 and treated as a small perturbation for the states of two CuO2 planes described by the t-t′-t″-J* model. In the generalized mean field approximation for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${d_{{x^2} - {y^2}}}$$\end{document} symmetry of the superconducting gap, neither the interlayer hopping or exchange interaction, nor the pair hopping between CuO2 layers provides an additional mechanism of Cooper pair formation or an increase in Tc. In the concentration dependence of Tc, the bilayer splitting of the upper Hubbard band of quasi-holes is manifested as two peaks with temperatures slightly lower than the maximum Tc for a single-layer cuprate. Interlayer antiferromagnetic spin correlations suppress bilayer splitting.