Cooper Pairing Revisited

TL;DR

This paper revisits Cooper pairing, showing that considering both two-particle and two-hole pairs leads to imaginary energies in an ideal Fermi gas, but finite-lifetime pairs with a gap emerge when using the BCS ground state, resembling plasmons.

Contribution

It clarifies the nature of Cooper pairs by including two-hole pairs and demonstrates the emergence of finite-lifetime, gapped pairs in the BCS framework.

Findings

Purely imaginary pair energy in ideal Fermi gas when ignoring two-hole pairs.

Finite-lifetime, gapped pairs appear in the BCS ground state.

Pair excitation energy rises linearly with momentum, similar to plasmons.

Abstract

We recall the fundamental fact that Cooper pairs defined without ignoring two- hole pairs along with two-particle ones leads to a purely imaginary pair energy when the problem is based on the ideal Fermi gas sea. However, bound finite- lifetime pairs are recovered when it is based on the BCS ground-state Fermi sea. Their excitation energy is gapped at zero total momenta and then rises linearly in either 2D or 3D, making them similar to 3D plasmons which however rise quadratically.