Perturbation Theory on the Superconductivity of Heavy Fermion Superconductor UPd_2Al_3

TL;DR

This study uses perturbation theory on a Hubbard model to analyze the superconducting mechanism and transition temperature of heavy fermion superconductor UPd_2Al_3, emphasizing the role of spin fluctuations and vertex corrections.

Contribution

It demonstrates that perturbation theory with respect to Coulomb interaction U can explain the superconductivity in UPd_2Al_3, highlighting the importance of vertex corrections.

Findings

Spin fluctuations induce d-wave pairing.

Vertex corrections are crucial for accurate transition temperatures.

Perturbation theory successfully explains superconductivity in UPd_2Al_3.

Abstract

We investigate the superconducting mechanism and the transition temperature of heav y fermion superconductor UPd_2Al_3 on the basis of a single band two-dimensional Hubbard model on triangular lattice, whi ch represents the most heavy band of UPd_2Al_3. Both normal and anomalous self-energies are calculated up to third order with respect to the Coulomb repulsion U between itinerant electrons. The superconducting transition temperature is obtained by solving the Eliashberg's equation. Reasonable transition temperatures are obtained for moderately large U. It is fou nd 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 tempe ratures. These results seem to show that the superconductivity in UPd_2Al_3 can be explained by the perturbation theory with respect to U.