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

TL;DR

This paper investigates the superconducting transition temperature and electronic properties of an organic superconductor using third order perturbation theory, finding good agreement with experiments and highlighting the importance of vertex corrections.

Contribution

It applies third order perturbation theory to model the superconducting properties of $$-type organic superconductors, comparing results with FLEX and emphasizing the role of vertex corrections.

Findings

Perturbation theory yields transition temperatures consistent with experiments.

FLEX predicts higher transition temperatures than perturbation theory.

Vertex corrections significantly affect $T_c$ in strongly frustrated systems.

Abstract

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.