Comment on "Boson-fermion model beyond the mean-field approximation"
R. Friedberg, H.C. Ren, and O. Tchernyshyov
TL;DR
This paper critiques a recent claim that boson-fermion models lack Cooper pairing, demonstrating that the claim is based on an inconsistent approximation and reaffirming the link between fermion pairing divergence and boson condensation.
Contribution
The paper clarifies the inconsistency in previous approximations and emphasizes the correct relationship between fermion pairing divergence and boson mode condensation in boson-fermion models.
Findings
The conjecture about absence of Cooper pairing is based on an invalid approximation.
Divergence of the fermion t-matrix indicates boson mode condensation.
The correct analysis supports the presence of pairing in boson-fermion models.
Abstract
In a recent paper [A.S.Alexandrov, J.Phys.:Condens.Matter 8, 6923 (1996); cond-mat/9603111], it has been suggested that there is no Cooper pairing in boson-fermion models of superconductivity. We show that this conjecture is based on an inconsistent approximation that violates an exact identity. Quite generally, the divergence of the fermion t-matrix (the Thouless criterion) is accompanied by the condensation of a boson mode.
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