Perturbation Theory on the Transition Temperature and Electronic Properties of Organic Superconductor

We study the superconducting transition temperature and the electronic properties of the metallic phase of $\kappa$-type (BEDT-TTF)$_2$X which shows unconventional properties in experiments, on the basis of the third order perturbation theory for a simple effective Hubbard model of a nearly triangular lattice. Appropriate transition temperatures and $d_{x^2-y^2}$ symmetry of the gap function are obtained in good agreement with experimental results. We also calculate the transition temperature by the fluctuation-exchange approximation(FLEX) in order to compare the two approaches; FLEX gives higher transition temperatures rather than the perturbation approach. However, it is also found that the vertex corrections, which are ignored in FLEX, have a crucial effect on $T_{\rm c}$ for strongly frustrated systems. The density of states and the normal self-energy calculated in this perturbation scheme show the nature of the conventional Fermi liquid near the Mott-insulator. Thus, our perturbation approach is applicable to the conventional metallic phase of this compound, while it cannot explain the (pseudo-)spin gap phenomenon which signals the non-Fermi liquid.