Competition between the Coulomb and phonon fields: superconductivity in a quiescent Fermi gas

Abstract

Co-existence of and competition between the screened Coulomb and phonon fields are fundamental facts in superconductors. In the conventional superconductors the strong screening greatly suppresses the Coulomb interaction and the phonon field that mediates a given attractive interaction between electrons may thus play a leading role. A quiescent Fermi sea hence applies, as proposed by Cooper and adopted in BCS.In this model a graphical derivative technique, based on Ward's identity, is developed to consider the contributions to the interparticle interaction. This technique allows one to evaluate the effective two-particle interaction (T-matrix). It is shown that the conventional Cooper instability in a quiescent Fermi gas is only caused by agivenattractive interaction. Of more importance is that the methodology presented in this work can be extended to the investigation of the intermediate and strong coupling cases where the well-known Migdal theorem is not applicable and the vertex corrections must be evaluated.