Systems with Condensates and Pairing

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Critical Parameters ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Pair Breaking ◽  
Systematic Theory ◽  
Bose Einstein Condensation ◽  
T Matrix ◽  
The Stability ◽  
Bose Einstein

The Bose–Einstein condensation and appearance of superfluidity and superconductivity are introduced from basic phenomena. A systematic theory based on the asymmetric expansion of chapter 11 is shown to correct the T-matrix from unphysical multiple-scattering events. The resulting generalised Soven scheme provides the Beliaev equations for Boson’s and the Nambu–Gorkov equations for fermions without the usage of anomalous and non-conserving propagators. This systematic theory allows calculating the fluctuations above and below the critical parameters. Gap equations and Bogoliubov–DeGennes equations are derived from this theory. Interacting Bose systems with finite temperatures are discussed with successively better approximations ranging from Bogoliubov and Popov up to corrected T-matrices. For superconductivity, the asymmetric theory leading to the corrected T-matrix allows for establishing the stability of the condensate and decides correctly about the pair-breaking mechanisms in contrast to conventional approaches. The relation between the correlated density from nonlocal kinetic theory and the density of Cooper pairs is shown.

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).

Cooper Pairing and Ladder Correlations in a BCS Ground State

2003 ◽  
Vol 17 (18n20) ◽  
pp. 3304-3309
Author(s):  
V. C. Aguilera-Navarro ◽  
M. Fortes ◽  
M. de Llano
Keyword(s):  
Ground State ◽  
Center Of Mass ◽  
Two Dimensions ◽  
Einstein Condensation ◽  
Positive Energy ◽  
Cooper Pairs ◽  
Linear Dispersion ◽  
Bose Einstein Condensation ◽  
Leading Term ◽  
Bose Einstein

A Bethe–Salpeter treatment of Cooper pairs (CPs) based on an ideal Fermi gas (IFG) "sea" produces unstable CPs if holes are not ignored. Stable CPs with damping emerge when the BCS ground state replaces the IFG, and are positive-energy, finite-lifetime resonances for nonzero center-of-mass momentum with a linear dispersion leading term. Bose–Einstein condensation of such pairs may thus occur in exactly two dimensions as it cannot with quadratic dispersion.

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.

scholarly journals Bose–Einstein condensation of nonzero-center-of-mass-momentum Cooper pairs

2001 ◽  
Vol 364-365 ◽  
pp. 161-165 ◽  
Author(s):  
J. Batle ◽  
M. Casas ◽  
M. Fortes ◽  
M.A. Solı́s ◽  
M. de Llano ◽  
...  
Keyword(s):  
Center Of Mass ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Bose Einstein Condensation ◽  
Bose Einstein

BCS-BEC CROSSOVER WITHOUT APPEAL TO SCATTERING LENGTH THEORY

2014 ◽  
Vol 28 (08) ◽  
pp. 1450054 ◽  
Author(s):  
G. P. MALIK
Keyword(s):  
Interaction Parameter ◽  
Scattering Length ◽  
Critical Values ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Bose Einstein Condensation ◽  
The Subject ◽  
Bose Einstein

BCS-BEC (an acronym formed from Bardeen, Cooper, Schrieffer and Bose–Einstein condensation) crossover physics has customarily been addressed in the framework of the scattering length theory (SLT), which requires regularization/renormalization of equations involving infinities. This paper gives a frame by frame picture, as it were, of the crossover scenario without appealing to SLT. While we believe that the intuitive approach followed here will make the subject accessible to a wider readership, we also show that it sheds light on a feature that has not been under the purview of the customary approach: the role of the hole–hole scatterings vis-à-vis the electron–electron scatterings as one goes from the BCS to the BEC end. More importantly, we show that there are critical values of the concentration (n)and the interaction parameter (λ) at which the condensation of Cooper pairs takes place; this is a finding in contrast with the view that such pairs are automatically condensed.

scholarly journals FURTHER EVIDENCE FOR LINEARLY-DISPERSIVE COOPER PAIRS

2006 ◽  
Vol 20 (17) ◽  
pp. 1067-1073 ◽  
Author(s):  
M. DE LLANO ◽  
J. J. VALENCIA
Keyword(s):  
Transition Temperature ◽  
Cuprate Superconductors ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Condensate Fraction ◽  
Bose Einstein Condensation ◽  
Depth Data ◽  
Fraction Versus ◽  
Bose Einstein ◽  
Special Case

A recent Bose–Einstein condensation (BEC) model of several cuprate superconductors is based on bosonic Cooper pairs (CPs) moving in 3D with a quadratic energy-momentum (dispersion) relation. The 3D BEC condensate-fraction versus temperature formula poorly fits penetration-depth data for two cuprates in the range 1/2<T/Tc≤1 where Tc is the BEC transition temperature. We show how these fits are dramatically improved, assuming cuprates to be quasi-2D, and how equally good fits are obtained for conventional 3D and quasi-1D nanotube superconducting data, provided the correct linear CP dispersion is assumed in BEC at their assumed corresponding dimensionalities. This is offered as additional concrete empirical evidence for linearly-dispersive pairs in another recent BEC scenario of superconductors within which a BCS condensate turns out to be a very special case.

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