Theory of Strong Coupling Superconductors

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One of the most important problems in the high temperature superconductors is the understanding of pseudogap phenomena. We have made clear the origin of the pseudogap by using the T-matrix approximation. The origin is the superconducting fluctuation due to the strong attractive interaction in the quasi-two dimensional system. Through this research we have successfully derived the pseudogap and superconducting gap above and below TィイD2cィエD2, respectively.The other important result obtained by our study is the explanation of origin of the superconductivity in strongly correlated electron systems. By using the perturbation theory we have successfully derived the superconducting state corresponding to each system; the d-wave gap state for the cuprates and the organic superconductor BEDT-TTF and the p-wave gap state for the triplet superconductor SrィイD22ィエD2RuOィイD24ィエD2. These facts show that the origin of superconductivity is the momentum dependence of the interaction originated from the Coulomb repulsion.Especially, theory of superconductivity in SrィイD22ィエD2RuOィイD24ィエD2 is very important. The critical temperature of superconductivity in the system is 1.5K. Even for this low TィイD2cィエD2 we can apply the perturbation theory and predict the appearance of superconductivity including the symmetry. Therefore, we have a powerful method to study the possibility of superconductivity in the strongly correlated systems. This is the most important finding of our study.