Coulomb correlations and pseudogap effects in a preformed pair model for the cuprates

Abstract

We extend previous work on pre-formed pair models of superconductivity to incorporate Coulomb correlation effects. For neutral systems, these models have provided a useful scheme which interpolates between BCS and Bose Einstein condensation with increasing coupling and thereby describes some aspects of pseudo-gap phenomena. However, charge fluctuations (via the plasmon, ωp) significantly modify the collective modes and therefore the interpolation behavior. We discuss the resulting behavior of the pseudo-gap and thermodynamic quantities such as Tc, χ and Cv as a function of ωp.The role of the pseudo-gap 1 in the high T c cuprates is emerging as an important indicator of the nature of the superconductivity as well as the normal state. There are two widely discussed but competing explanations for pseudo-gap effects but no clear and decisive experiments to support one scenario over the other. Early observations associated the pseudo-gap with magnetic pairing 2 above T c (often called the "spin gap"). It is now clear, however, that some form of normal state pairing is seen in photoemission as well as charge transport data. Moreover, at least in the photoemission data the pseudo-gap appears to have the d-wave symmetry 1 of the ordered state and this leads naturally to the association of this "gap" with precursor superconductivity. 3-5 This second scenario is further supported by the observation of low dimensionality and short coherence lengths in high T c superconductors, which suggests important deviations from ideal mean field or BCS transitions. Indeed, the approach of the present paper assumes the precursor superconductivity scenario, in large part because it is important to establish, at least as a base-line, the extent to which such superconducting "fluctuation" effects may be responsible for pseudo-gap behavior.Among those models which subscribe to a precursor superconductivity scenario there are additionally two rather distinct viewpoints. Emery and Kivelson 5 have argued that the pseudo-gap state of the cuprates is similar to that observed in granular films where phase coherence is not fully established, although large regions of the material have a well established superconducting amplitude. Because it is small, in some sense, in the cuprates their approach focuses on n/m * or alternatively on the plasma frequency ω p as the key "phase stiffness" parameter. Alternatively, others 3,4,6,7 have focused on the observed small size of the superconducting correlation length ξ to argue for important corrections to BCS theory associated with pre-formed or nearly-formed pairs 8 which exist well above T c and therefore give rise to significant pseudo-gap effects. The present paper is based on the viewpoint that in the cuprates the characteristic parameter of the charge degrees of freedom, n/m * or equivalently ω p , should be treated on a relatively equal footing with the correlation length, ξ.To study the role of Coulomb interactions on pseudogap phenomena, we adopt a natural microscopic framework which incoporates ch...

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