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 CuO2 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 Tc the connection between different singular points becomes increasingly less important, and the electrons become more one-dimensional. Other explanations are briefly discussed. copyright 1997 The American Physical Society