Phase fluctuations and pseudogap phenomena

This article reviews the current status of precursor superconducting phase fluctuations as a possible mechanism for pseudogap formation in high-temper ature superconducrors. In particular we compare this approach which relies on the two-dimensional nature of the superconductivity to the often used T- matrix approach. Starting from simple pairing Hamiltonians we present a bro ad pedagogical introduction to the BCS-Bose crossover problem. The finite t emperature extension of these models naturally leads to a discussion of the Berezinskii-Kosterlitz-Thouless superconducting transition and the related phase diagram including the effects of quantum phase fluctuations and impu rities. We stress the differences between simple Bose-BCS crossover theorie s and the current approach where one can have a large pseudogap region even at high carrier density where the Fermi surface is well-defined. Green's f unction and its associated spectral function, which explicitly show non-Fer mi liquid behavior, is constructed in the presence of vortices. Finally dif ferent mechanisms including quasi-particle-vortex and vortex-vortex interac tions for the filling of the gap above T, are considered. (C) 2001 Elsevier Science B.V. All rights reserved.