Phase transition between d-wave and anisotropic s-wave gaps in high temperature oxides superconductors

Abstract

We study models for superconductivity with two interactions: $V^{>}$ due to antiferromagnetic(AF) fluctuations and $V^{<}$ due to phonons, in a weak coupling approach to the high temperature superconductivity. The nature of the two interactions are considerably different; $V^{>}$ is positive and sharply peaked at ($\pm \pi$,$\pm \pi$) while $V^{<}$ is negative and peaked at ($0,0$) due to weak phonon screening. We numerically find (a) weak BCS attraction is enough to have high critical temperature if a van Hove anomaly is at work, (b) $V^{>}$ (AF) is important to give d-wave superconductivity, (c) the gap order parameter $\Delta (\mathbf{k})$ is constant(s-wave) at extremely overdope region and it changes to anisotropic s-wave as doping is reduced, (d) there exists a first order phase transition between d-wave and anisotropic s-wave gaps. These results are qualitatively in agreement with preceding works; they should be modified in the strongly underdope region by the presence of antiferromagnetic fluctuations and ensuing AF pseudogap.

4 pages in RevTex (double column), 4 figures

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