FIVE POSSIBLE REASONS WHY HIGH-Tc SUPERCONDUCTIVITY IS STALLED

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2313-2323
Author(s):  
M. GRETHER ◽  
M. DE LLANO
Keyword(s):  
Microscopic Theory ◽  
Bcs Theory ◽  
Einstein Condensation ◽  
Critical Temperatures ◽  
Electron Pairs ◽  
High Tc ◽  
Bose Einstein Condensation ◽  
Phonon Mechanism ◽  
Bose Einstein ◽  
Theory Of Superconductivity

Five commonly held premises considered questionable assumptions in the microscopic theory of superconductivity are discussed as possible reasons why the search appears to be stalled for a theoretical framework, admittedly ambitious, capable of predicting materials with critical temperatures Tc higher than the 1993 record of 164K in HgTlBaCaCuO (under pressure). We focus the dilemma as a whole in terms of a generalized Bose-Einstein condensation (GBEC) interpretation that includes and further extends BCS theory, as well as substantially enhancing its predicted Tcs within the electron-phonon mechanism producing pairing. The new GBEC model is an extension of the Friedberg-T.D. Lee 1989 boson-fermion BEC theory of high-Tc superconductors in that it includes hole pairs as well as electron pairs.

Entropy and heat capacity in the generalized Bose–Einstein condensation theory of superconductors

2019 ◽  
Vol 33 (26) ◽  
pp. 1950311
Author(s):  
L. A. García ◽  
M. de Llano
Keyword(s):  
Heat Capacity ◽  
Energy Gap ◽  
Coupling Parameter ◽  
Bcs Theory ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Total Electron ◽  
Bose Einstein Condensation ◽  
Unpaired Electrons ◽  
Bose Einstein

The new generalized Bose–Einstein condensation (GBEC) quantum-statistical theory starts from a noninteracting ternary boson-fermion (BF) gas of two-hole Cooper pairs (2hCPs) along with the usual two-electron Cooper pairs (2eCPs) plus unpaired electrons. Here we obtain the entropy and heat capacity and confirm once again that GBEC contains as a special case the Bardeen–Cooper–Schrieffer (BCS) theory. The energy gap is first calculated and compared with that of BCS theory for different values of a new dimensionless coupling parameter n/n[Formula: see text] where n is the total electron number density and n[Formula: see text] that of unpaired electrons at zero absolute temperature. Then, from the entropy, the heat capacity is calculated. Results compare well with elemental-superconductor data suggesting that 2hCPs are indispensable to describe superconductors (SCs).

GENERALIZED BOSE-EINSTEIN CONDENSATION IN SUPERCONDUCTIVITY

2010 ◽  
Vol 24 (25n26) ◽  
pp. 5163-5171
Author(s):  
MANUEL de LLANO
Keyword(s):  
Spin Fluctuation ◽  
Interaction Model ◽  
Bcs Theory ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Condensation Energy ◽  
Weakly Bound ◽  
Bose Einstein Condensation ◽  
Fermi Temperature ◽  
Bose Einstein

Unification of the BCS and the Bose-Einstein condensation (BEC) theories is surveyed in detail via a generalized BEC (GBEC) finite-temperature statistical formalism. Its major difference with BCS theory is that it can be diagonalized exactly. Under specified conditions it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero-temperature condensation energy for all couplings, thereby suggesting that a BCS condensate is a BE condensate in a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly-bound two-electron and two-hole Cooper pairs. Without abandoning the electron-phonon mechanism in moderately weak coupling it suffices, in principle, to reproduce the unusually high values of Tc (in units of the Fermi temperature TF) of 0.01-0.05 empirically reported in the so-called "exotic" superconductors of the Uemura plot, including cuprates, in contrast to the low values of Tc/TF ≤ 10-3 roughly reproduced by BCS theory for conventional (mostly elemental) superconductors. Replacing the characteristic phonon-exchange Debye temperature by a characteristic magnon-exchange one more than twice in size can lead to a simple interaction model associated with spin-fluctuation-mediated pairing.

BEC-DRIVEN SUPERCONDUCTIVITY IN THE CUPRATES

1999 ◽  
Vol 13 (29n31) ◽  
pp. 3489-3491 ◽  
Author(s):  
M. CASAS ◽  
A. PUENTE ◽  
A. RIGO ◽  
M. J. DAVIDSON ◽  
R. M. QUICK ◽  
...  
Keyword(s):  
Helmholtz Free Energy ◽  
Center Of Mass ◽  
Two Dimensions ◽  
Bcs Theory ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Critical Temperatures ◽  
Model Interaction ◽  
Fermion Number ◽  
Bose Einstein

We apply to cuprates a three-fluid ideal boson-fermion statistical model of superconductivity in two dimensions (2D) derived from three extrema of the system Helmholtz free energy (subject to constant total fermion-number) for the BCS model interaction between fermions. The same interactions absent in BCS theory are neglected here. As the ensuing bosonic Cooper pairs move not in vacuum but in a Fermi sea we employ the correct linear — as opposed to the commonly-assumed quadratic — dispersion relation in the center-of-mass momentum (CMM). More importantly, pair breakup beyond a certain (very small) CMM is accounted for. Bose–Einstein condensation (BEC) critical temperatures of about 800 K result for moderate coupling with cuprate parameters.

scholarly journals The effect of non-local derivative on Bose-Einstein condensation

2021 ◽  
Vol 24 (1) ◽  
pp. 13002
Author(s):  
F. E. Bouzenna ◽  
M. T. Meftah ◽  
M. Difallah
Keyword(s):  
Transition Temperature ◽  
Free Particle ◽  
Ideal Gas ◽  
Einstein Condensation ◽  
Critical Temperatures ◽  
Bose Einstein Condensation ◽  
Non Local ◽  
The Moment ◽  
Bose Einstein ◽  
Local Derivative

In this paper, we study the effect of non-local derivative on Bose-Einstein condensation. Firstly, we consider the Caputo-Fabrizio derivative of fractional order α to derive the eigenvalues of non-local Schrödinger equation for a free particle in a 3D box. Afterwards, we consider 3D Bose-Einstein condensation of an ideal gas with the obtained energy spectrum. Interestingly, in this approach the critical temperatures Tc of condensation for 1 < α < 2 are greater than the standard one. Furthermore, the condensation in 2D is shown to be possible. Second and for comparison, we presented, on the basis of a spectrum established by N. Laskin, the critical transition temperature as a function of the fractional parameter α for a system of free bosons governed by an Hamiltonian with power law on the moment (H~pα). In this case, we have demonstrated that the transition temperature is greater than the standard one. By comparing the two transition temperatures (relative to Caputo-Fabrizio and to Laskin), we have found for fixed α and the density ρ that the transition temperature relative to Caputo-fabrizio is greater than relative to Laskin.

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