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

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.

Diagrammatic quantum Monte Carlo solution of the two-dimensional cooperon-fermion model

“…1) is a basic model for superconductivity that has widely been adopted to explain the BCS-BEC crossover in ultra-cold fermionic atomic gases [1][2][3] and high-T c superconductivity. 1,[4][5][6][7][8][9][10][11][12][13][14] The resonantly paired fermions, or cooperons, in this model can either be locally bound pairs of small polarons due to extremely strong electronphonon coupling, 15 or localized Cooper pairs due to strong local pairing as might be the case in high-T c superconductors 12 , or molecular bosons in ultra-cold atoms. [1][2][3] The potential existence of finite energy cooperons with a local attraction has also been put forward a few years ago in a simple semiconductor system.…”

Constraints on the total coupling strengthto bosons in the iron based superconductors

“…This special situation might be well described for coexisting Cooper paoirs and bipolarons by the so ‐called s ‐channel theory in terms of Mandelstam variables (sometimes also denoted as Boson (Fermion) model) where the bipolarons exist above as resonance states, only, but start to condense at together with the Cooper pairs and the gap is given by the total condensate density. A strong coupling (and even a multiband weak ‐coupling) generalization of that approach has not been investigated theoretically in detail to the best of our knowledge, despite its criticism for by Alexandrov who favors instead a (bi) polaronic in case of a specific el–ph interaction in the Holstein model . The corresponding analysis for spin ‐polarons is missing at all to best of our knowledge.…”

Are preformed Cooper pairs the cause for the pseudogap in superconductors?

“…Analytical continuation from the real axis to the imaginary axis (by substituting −→ iω n ) makes evident that the contribution to the 'bare boson' energy E Q given by the second term in rhs of (7) coincides with the boson self-energy cited in Ref. [23] which was established with a diagrammatic technique for a hamiltonian such as (1) (without H U ) but in an entirely different context.…”

“…Ref. [22,23]) in terms of creation/annihilation operators for fermions (a operators) and bosons (b operators). Then, one has…”