Superconductivity in the exactly solvable model of pseudogap state: The absence of self-averaging

The features of the superconducting state are studied in the simple exactly solvable model of the pseudogap state induced by fluctuations of the short-range “dielectric” order in the model of the Fermi surface with “hot” spots. The analysis is carried out for arbitrary short-range correlation lengths ξ_corr. It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature T _c of the uniform superconducting transition in the entire sample, which is a consequence of non-self-averaging of the superconducting order parameter over the random fluctuation field. In the temperature range T>T _c, superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξ_corr; in particular, the range of existence for drops becomes narrower and vanishes as ξ_corr → 0, but for finite values of ξ_corr, complete self-averaging does not take place.