Effect of temperature on the energy gap in a superconductivity model using U-centers

According to the theory of U-centers, a strong electron-lattice interaction can lead to the fact that the binding energy of two electrons at certain temperatures is higher than the energy of their Coulomb repulsion and, therefore, the possibility of the formation of Cooper pairs appears. If these pairs move coherently without falling apart, then superconductivity occurs. In this work using the Hubbard Hamiltonian and applying the secondary quantization method, we calculate the temperature dependence of the superconducting gap Δ = Δ(T). A temperature dependence of the HTSC resistance in the normal state demonstrates the features of both semiconductor and metallic behavior. It is known that high-temperature superconductors exhibit such properties only in the normal state. In the work presented now, using mathematical calculations, we discuss the presence of four regions of the HTSC phase diagram T = T(ν), where ν is the relative concentration of U-centers. The formation mechanisms of negative U-centers are not considered here. We only assume that they are present in HTSC. (paper)