Theory of Superconductivity in Strongly correlated Electron Systems

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This year is the last year for our project. We are completing our research on superconductivity in strongly correlated electron systems. Our theory concludes the following points.1.Transition temperature of superconductivity is determined by the momentum dependence of electron interaction originating from the Coulomb repulsion U and mass enhancement factor 1/z.2.We have calculated up to the fourth order terms of self-energy terms. The fourth order terms play essential roles in giving actual mass enhancement factor.3.By using the forth order perturbation theory we can derive the Dyson-Gorkov Equation. By solving this equation we can discuss the roles of renormalization factor and anisotropic interaction between quasi-particles.4.We can explain the reason why Tc in LSCO is lower than that in YBCO. The reason is the renormalization factor z which is inverse of the mass-enhancement factor. The renormalization factor z in LSCO is smaller than that in YBCO, owing to the strong electron correlation in LSCO. Since the energy scale of qusi-particles is determined by z, the gap and Tc are determined by z.5.This kind of renormalization is general in all the strongly correlated electron systems. We can explain Tc in organic superconductors and heavy fermions.