Superconductivity in the pseudogap state in the hot spot model: The influence of impurities and the phase diagram

We analyze the peculiarities of the superconducting state (s- and d-wave paring) in the model of the pseudogap state induced by Heisenberg antiferromagnetic short-range order spin fluctuations. The model is based on the pattern of strong scattering near hot spots at the Fermi surface. The analysis is based on the microscopic derivation of the Ginzburg-Landau expansion with the inclusion of all Feynman diagrams of perturbation theory for the interaction of an electron with short-range order fluctuations and in the ladder approximation for the scattering by normal (nonmagnetic) impurities. We determine the dependence of the critical superconducting transition temperature and other superconductor characteristics on the pseudogap parameters and the degree of impurity scattering. We show that the characteristic shape of the phase diagram for high-temperature superconductors can be explained in terms of the model under consideration.