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Research & Reviews: Journal of Material Sciences | ISSN: 2321-6212 | Volume 6
Theoretical, Materials and Condensed Matter Physics
5
th
International Conference on
November 26-28, 2018 | Los Angeles, USA
Cooper pairs in superconductivity in a generalized BEC theory
I Chávez, LA García, M Grether
and
M de Llano
Universidad Nacional Autónoma de México, México
T
he generalized Bose-Einstein condensation (GBEC) theory subsumes as special cases both BCS and BEC, among other
theories. It hinges on three separate new ingredients: i) treating Cooper pairs (CPs) as
actual
bosons as distinct from BCS
pairs which strictly speaking are not bosons; ii) inclusion of two-hole Cooper pairs (2hCPs) on an equal footing with the
usual two-electron ones (2eCPs); and iii) incorporating in the resulting ideal
ternary
boson-fermion (BF) gas specific vertex
interactions that drive formation/dis-integration processes of both kinds of CPs. Here we extend the BCS-Bose crossover
theory by
explicitly
including 2hCPs. This leads to a phase diagram with two pure phases, one with 2eCPs and the other with
2hCPs, plus a mixed phase with arbitrary proportions of both. The special-case phase with a 50-50 mixture of both 2e/2hCPs
gives the usual
unextended
BCS-Bose crossover theory. Furthermore, if
T
c
and
T
F
are respectively the critical and the Fermi
temperatures, it predicts
T
c
/T
F
values for the elemental superconductors Al, In, Sn, Pb, Hg, and Nb comparing quite well with
experiment and notably much better than BCS predictions. Also shown is a phase diagram of the dimensionless energy gap at
zero-temperature Δ(0)/
E
F
vs n/n
f
, where
E
F
=k
B
T
F
is the Fermi energy. We do this for the 50-50 case as well as for the pure 2eCPs
and 2hCPs cases separately. It is thus unequivocally shown that if one ignores 2hCPs the energy gap lies substantially below the
50-50 case which already roughly reproduces the data.
Biography
I Chávez MS and BS have completed his Doctoral degree in the Material Sciences and Engineering Research Graduate Program at the National Autonomous
University of Mexico (UNAM, in Spanish) with the thesis titled “
A new dimensionless coupling constant in superconductivity
.” He is also a Laboratory Assistant at
the School of Sciences at UNAM.
israelito@ciencias.unam.mxI Chávez et al., Res. Rev. J Mat. Sci. 2018, Volume 6
DOI: 10.4172/2321-6212-C10-041