Superconductivity in the "Hot Spots" Model of the Pseudogap State: Impurity Scattering and Phase Diagram

We analyze the anomalies of superconducting state (both s- and d-wave pairing) in the model of the pseudogap state induced by Heisenberg spin fluctuations of antiferromagnetic short-range order, and based on the scenario of strong scattering near the "hot spots" on the Fermi surface. We present microscopic derivation of Ginzburg-Landau expansion, taking into account all Feynman graphs of perturbation theory for electron interaction with fluctuations of short-range order and in the "ladder" approximation for electron scattering by normal (nonmagnetic) impurities. We determine the dependence of superconducting critical temperature T_c and other characteristics of a superconductor on the parameters of the pseudogap and impurity scattering. It is shown that within this model it is possible to explain the typical phase diagram of high- temperature superconductors.