Perturbation theory of the superconductivities in heavy fermion systems Original Research Article

We investigate the superconducting mechanism and the transition temperature Tc of heavy fermion superconductor UPd2Al3 and CeIrxCo1−xIn5 on the basis of a single band two-dimensional Hubbard model, which represents the most heavy band, respectively. Both normal and anomalous self-energies are calculated up to third order with respect to the Coulomb repulsion U. Reasonable transition temperatures are obtained for moderately large U by solving the Éliashbergʹs equation. 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. We point out that it is reasonable to treat the electron correlation by perturbation theory based on Fermi liquid theory, in calculating Tc of typical heavy fermion superconductors.