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-temperature 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 broad pedagogical introduction to the BCS-Bose crossover problem. The finite temperature 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 impurities. We stress the differences between simple Bose-BCS crossover theories 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 function and its associated spectral function, which explicitly show non-Fermi liquid behavior, is constructed in the presence of vortices. Finally different mechanisms including quasi-particle-vortex and vortex-vortex interactions for the filling of the gap above T, are considered. (C) 2001 Elsevier Science B.V. All rights reserved.