Superconductivity in an Exactly Solvable Model of the Pseudogap State: Absence of Self Averaging
Abstract
We analyze the anomalies of superconducting state within a simple exactly solvable model of the pseudogap state, induced by fluctuations of ``dielectric'' short range order, for the model of the Fermi surface with ``hot'' patches. The analysis is performed for the arbitrary values of the correlation length xicorr of this short range order. It is shown that superconducting energy gap averaged over these fluctuations is non zero in a wide temperature range above Tc - the temperature of homogeneous superconducting transition. This follows from the absence of self averaging of the gap over the random field of fluctuations. For temperatures T>Tc superconductivity apparently appears in separate regions of space (``drops''). These effects become weaker for shorter correlation lengths xicorr and the region of ``drops'' on the phase diagram becomes narrower and disappears for xicorr-->0, however, for the finite values of xicorr the complete self averaging is absent.
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