Ginzburg-Landau equations for the extended saddle-point model

Ginzburg-Landau-type equations are derived describing the model of tetragonal high-temperature superconducting cuprates based on the dominant role of extended saddle-point singularities in the electron spectrum and the assumption that the interaction between electrons consists of a strong long-range phonon-mediated attraction and a weak short-range repulsion. The connection between ${\mathrm{CuO}}_2$ layers is assumed to be established by resonant tunneling. As an example, the temperature dependence of the upper critical field along the $c$ axis is calculated, which appears to have a positive curvature, as observed in many experiments. This is explained by the fact that with departure from $T_c$ the connection between different singular points becomes increasingly less important, and the electrons become more one-dimensional. Other explanations are briefly discussed.