Perturbation Theory on the Superconductivity of Heavy Fermion Superconductors CeIr_{x}Co_{1-x}In_5

Abstract

We reformulate the Eliashberg's equation for the superconducting transition within the quasi-particle description, which takes account of the heavy electron mass. We discuss the superconductivity of CeIr_{x}Co_{1-x}In_5 by using such a renormalized formula. On the basis of an effective two-dimensional Hubbard model which represents the most heavy quasi-two dimensional Fermi surface with f-character of CeIr_{x}Co_{1-x}In_5, both normal and anomalous self-energies are calculated up to third order with respect to the renormalized on-site repulsion U between quasi-particles. The superconducting transition temperature is obtained by solving the Eliashberg's equation. Reasonable transition temperatures are obtained for moderately large U. It is found that the momentum and frequency dependence of spin fluctuations given by RPA-like terms gives rise to the d-wave pairing state, while the vertex correction terms are important for obtaining reasonable transition temperatures and for differentiating n-dependence of T_c. These obtained results seem to explain the x-dependence of T_c in CeIr_{x}Co_{1-x}In_5 and confirm the usefulness of the perturbation theory with respect to U.