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Extended BCS-Bose Crossover

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Abstract

Applying the generalized Bose-Einstein condensation (GBEC) formalism, we extend the BCS-Bose crossover theory by explicitly including hole Cooper pairs (2hCPs). From this, follows a phase diagram with two pure phases, one with 2hCPs and the other with electron Cooper pairs (2eCPs), plus a mixed phase with arbitrary proportions of 2eCPs and 2hCPs. The special-case phase when there is perfect symmetry, i.e., with ideal 50-50 proportions between 2eCPs and 2hCPs, corresponds to the usual BCS-Bose crossover. Explicitly including 2hCPs yields an extended BCS-Bose crossover which predicts improved T c /T F values for some conventional superconductors (i.e., with electron-phonon dynamics) when compared with experiment. To do this, we employ the BCS dimensionless coupling constant λ B C S via the BCS gap equation and compare with the Bogoliubov et al. upper limit λ B C S ≤ 1/2. Another phase diagram presented exhibits experimental T c /T F values for some conventional superconductors for arbitrary proportions between 2eCPs and 2hCPs as function of Δn = n/n f − 1, where n is the electron concentration and n f that of unbound electrons at T = 0. The extended crossover is compared with experimental T c /T F values as well as to the gap-to- T c ratio.

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Acknowledgements

We thank G.C. Strinati for having called Refs. [1, 2] to our attention. IC and LAG thanks CONACyT (Mexico) for postgraduate grant 291001 and 403765, respectively. MG and MdeLl thank PAPIIT-DGAPA-UNAM (Mexico) for research grants IN116914 and IN100314, respectively.

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Authors and Affiliations

  1. Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apdo. Postal 70-360, 04360, Mexico City, Mexico

    I. Chávez, L. A. García & M. de Llano

  2. Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510, Mexico City, Mexico

    M. Grether

  3. N.E. Baumann State Technical University, Moscow, Russia

    V. V. Tolmachev

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  1. I. Chávez
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  2. L. A. García
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  3. M. Grether
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  4. M. de Llano
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  5. V. V. Tolmachev
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Correspondence to I. Chávez.

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Chávez, I., García, L.A., Grether, M. et al. Extended BCS-Bose Crossover. J Supercond Nov Magn 31, 631–637 (2018). https://doi.org/10.1007/s10948-017-4383-z

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  • DOI: https://doi.org/10.1007/s10948-017-4383-z

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