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

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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.

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Authors and Affiliations

  1. Department of Physics, Loughborough University, LE11 3TU, Loughborough, UK

    A. S. Alexandrov

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  1. A. S. Alexandrov
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Correspondence to A. S. Alexandrov.

Additional information

Received: 26 February 2004, Published online: 18 June 2004

PACS:

74.20.-z Theories and models of superconducting state - 74.20.Mn Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.) - 74.20.Rp Pairing symmetries (other than s-wave) - 74.25.Dw Superconductivity phase diagrams

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Alexandrov, A.S. Pairing of bosons in the condensed state of the boson-fermion model. Eur. Phys. J. B 39, 55–60 (2004). https://doi.org/10.1140/epjb/e2004-00170-5

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