Pairing of bosons in the condensed state of the boson-fermion model

TL;DR

This paper investigates the boson-fermion model for high-temperature superconductivity and superfluidity, revealing the absence of fermion pairing in 2D, flaws in mean-field approximations, and the existence of boson pairing with three coupled condensates in 3D.

Contribution

It demonstrates the failure of mean-field theory in the boson-fermion model and uncovers boson pairing and multiple condensates beyond previous approximations.

Findings

No fermion pairing or condensation in 2D for any symmetry.

Mean-field expansion yields no linear term and zero upper critical field.

Boson pairing analogous to Cooper pairing is found in 3D.

Abstract

A two component model of negative U centers coupled with the Fermi sea of itinerant fermions is discussed in connection with high-temperature superconductivity of cuprates, and superfluidity of atomic fermions. We examine the phase transition and the condensed state of this boson-fermion model (BFM) beyond the ordinary mean-field approximation in two and three dimensions. No pairing of fermions and no condensation are found in two-dimensions for any symmetry of the order parameter. The expansion in the strength of the order parameter near the transition yields no linear homogeneous term in the Ginzburg-Landau-Gor'kov equation and a zero upper critical field in any-dimensional BFM, which indicates that previous mean-field discussions of the model are flawed. Normal and anomalous Green's functions are obtained diagrammatically and analytically in the condensed state of a simplest version of 3D BFM. A pairing of bosons analogous to the Cooper pairing of fermions is found. There are three coupled condensates in the model, described by the off-diagonal single-particle boson, pair-fermion and pair-boson fields. These results negate the common wisdom that the boson-fermion model is adequately described by the BCS theory at weak coupling.