Electron-Phonon Interaction and Superconductivity in Heavy Electron Systems

Abstract

In heavy electron systems, because of the strong renormalization of the electronic states by electron-electron interaction, the electron-phonon coupling is much reduced. As a result vertex corrections by the electron-phonon interaction is negligible for the electron-phonon interaction vertex with frequency of phonon proper for quasiparticle pairing, although the usual Migdal's theorem no longer holds as a result of the reduction of the Fermi energy. By solving the Eliashberg equation and taking account of the Grüneisen parameter, we show that it is difficult to attribute the origin of the attractive interaction responsible for superconductivity to the electron-phonon interaction. On the other hand, the Coulomb interaction between quasiparticles is shown to maintain the coupling constant of the same order as that before the renormalization, and can be considered as the possible origin of the anisotropic superconductivity.