Pairing instability in an interacting Fermi gas

Abstract

The Cooper instability in an interacting Fermi gas is examined by using the perturbational diagram approach. A graphical derivative method based on Ward's identity is introduced to represent the contributions to the interparticle interactions from different channels. It is shown that pairing instability for the electrons excited from the Fermi sea may happen as a result of the presence of holes even when the original interaction is repulsive. Thus, in contrast to the Cooper instability caused by a given attractive interaction, the pairing instability can be induced by the particle - hole excitations. The application of the results to a layered two-dimensional Fermi gas is considered.

A pairing mechanism in superconductivity due to the screened coulomb field

“…We have attempted to deal with the normal state and phase transition from a metal to a superconductor for both cases of weak and strong coupling of electrons in a unified manner in a lengthy paper to be published somewhere else [8]. However, in this article, instead of the more rigorous and complicated Feynman diagrams, we propose a new mechanism of pairing, developing the original Cooper pairing, from which the two-particle effective interaction or T-matrix can be calculated as well.…”

“…It is of interest to note that this rather simple treatment leads to the same results as those from the rigorous perturbative analysis in the first step beyond the RPA and therefore can serve as its first approximation. We also present the major result, neglecting the tediously long derivations, from our treatment of the vertex function beyond the RPA [8,9].…”

“…We think, the phonon and the screened Coulomb fields concurrently exist and the interactions between quasiparticles (quasiholes) that lead to pairing is mediated either by phonons or by the screened Coulomb field depending on the competition between two fields [8]. In the conventional superconductors phonon plays a leading role as described by BCS, while in HTSs it seems that the screened Coulomb field overwhelms in the most of cases.…”

“…This becomes possible because the renormalized Coulomb interaction that was previously repulsive between two electrons can change its sign due to the many-particle effects: exchange-correlation effects. More details can be found in the work [8,12] by the authors. Thus, the electron pairing in our model is analogous to the electron coupling in the positronium molecule-like (biexciton) structure.…”

“…Note that there are two possibilities for the final momentum of an electron (hole) after scattering: it is either equal to or different from the initial momentum. If one really draws the scattering diagrams for the two cases, one will find that the boson propagators [8,11] in the two cases are different: D(k9q) and D(k9q)D(q9k). This minor discrepancy indeed leads to a great impact on the final result.…”