BCS-Bose crossover theory extended with hole Cooper pairs

2017 ◽  
Vol 31 (25) ◽  
pp. 1745013 ◽  
Author(s):  
I. Chávez ◽  
L. A. García ◽  
M. de Llano ◽  
M. Grether
Keyword(s):  
Einstein Condensation ◽  
Dimensionless Number ◽  
Cooper Pairs ◽  
Number Density ◽  
Phonon Dynamics ◽  
Perfect Symmetry ◽  
Pure Phases ◽  
Bose Einstein ◽  
Special Case ◽  
Hole Cooper Pairs

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. One has a special-case phase when there is perfect symmetry (i.e., with ideal 50–50 proportions between 2eCPs and 2hCPs). Explicitly including 2hCPs leads to an extended BCS-Bose crossover which predicts [Formula: see text] values for some well-known conventional superconductors (SCs) (i.e., assuming electron–phonon dynamics). These compare reasonably well with experimental data. We compare with experimental [Formula: see text] values for some conventional SCs associated with the new dimensionless number density [Formula: see text] with theoretical curves associated with the extended crossover for the special case of perfect symmetry. They all obey the Bogoliubov et al. upper limit, thus vindicating it.

Role of superconducting energy gap in extended BCS-Bose crossover theory

2017 ◽  
Vol 31 (25) ◽  
pp. 1745004 ◽  
Author(s):  
I. Chávez ◽  
L. A. García ◽  
M. de Llano ◽  
M. Grether
Keyword(s):  
Energy Gap ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Number Density ◽  
Superconducting Energy Gap ◽  
Special Cases ◽  
Bose Einstein ◽  
Hole Cooper Pairs ◽  
Theory Of Superconductivity

The generalized Bose–Einstein condensation (GBEC) theory of superconductivity (SC) is briefly surveyed. It hinges on three distinct new ingredients: (i) Treatment of Cooper pairs (CPs) as actual bosons since they obey Bose statistics, in contrast to BCS pairs which do not obey Bose commutation relations; (ii) inclusion of two-hole Cooper pairs (2hCPs) on an equal footing with two-electron Cooper pairs (2eCPs), thus making this a complete boson–fermion (BF) model; and (iii) inclusion in the resulting ternary ideal BF gas with particular BF vertex interactions that drive boson formation/disintegration processes. GBEC subsumes as special cases both BCS (having its 50–50 symmetry of both kinds of CPs) and ordinary BEC theories (having no 2hCPs), as well as the now familiar BCS-Bose crossover theory. We extended the crossover theory with the explicit inclusion of 2hCPs and construct a phase diagram of [Formula: see text] versus [Formula: see text], where [Formula: see text] and [Formula: see text] are the critical and Fermi temperatures, [Formula: see text] is the total number density and [Formula: see text] that of unbound electrons at [Formula: see text]. Also, with this extended crossover one can construct the energy gap [Formula: see text] versus [Formula: see text] for some elemental SCs by solving at least two equations numerically: a gap-like and a number equation. In 50–50 symmetry, the energy gap curve agrees quite well with experimental data. But ignoring 2hCPs altogether leads to the gap curve falling substantially below that with 50–50 symmetry which already fits the data quite well, showing that 2hCPs are indispensable to describe SCs.

INTRIGUING ROLE OF HOLE-COOPER-PAIRS IN SUPERCONDUCTORS AND SUPERFLUIDS

2008 ◽  
Vol 22 (25n26) ◽  
pp. 4367-4378 ◽  
Author(s):  
M. GRETHER ◽  
M. de LLANO ◽  
S. RAMÍREZ ◽  
O. ROJO
Keyword(s):  
Free Energy ◽  
Helmholtz Free Energy ◽  
Bcs Theory ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Superconducting Transition ◽  
Electron Phonon Interaction ◽  
Bose Einstein ◽  
Hole Cooper Pairs

The role in superconductors of hole-Cooper-pairs (CPs) are examined and contrasted with the more familiar electron-CPs, with special emphasis on their “background” effect in enhancing superconducting transition temperatures Tc — even when electron-CPs drive the transition. Both kinds of CPs are, of course, present at all temperatures. An analogy is drawn between the hole CPs in any many-fermion system with the antibosons in a relativistic ideal Bose gas that appear in substantial numbers only at higher and higher temperatures. Their indispensable role in yielding a lower Helmholtz free energy equilibrium state is established. For superconductors, the problem is viewed in terms of a generalized Bose-Einstein condensation (GBEC) theory that is an extension of the Friedberg-T.D. Lee 1989 boson-fermion BEC theory of high-Tc superconductors in that the GBEC theory includes hole CPs as well as electron-CPs — thereby containing as well as further extending BCS theory to higher temperatures with the same weak-coupling electron-phonon interaction parameters. We show that the Helmholtz free energy of both 2e- and 2h-CP pure condensates has a positive second derivative, and are thus stable equilibrium states. Finally, it is conjectured that the role of hole pairs in ultra-cold fermionic atom gases will likely be negligible because the very low densities involved imply a “shallow” Fermi sea.

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.

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 The Dirac Spectrum and the BEC-BCS Crossover in QCD at Nonzero Isospin Asymmetry

Particles ◽  
2020 ◽  
Vol 3 (1) ◽  
pp. 80-86
Author(s):  
Bastian B. Brandt ◽  
Francesca Cuteri ◽  
Gergely Endrődi ◽  
Sebastian Schmalzbauer
Keyword(s):  
Chemical Potential ◽  
Einstein Condensation ◽  
Complex Spectrum ◽  
Cooper Pairs ◽  
Zero Temperature ◽  
Isospin Asymmetry ◽  
Dirac Spectrum ◽  
Pion Condensation ◽  
Charged Pions ◽  
Bose Einstein

For large isospin asymmetries, perturbation theory predicts the quantum chromodynamic (QCD) ground state to be a superfluid phase of u and d ¯ Cooper pairs. This phase, which is denoted as the Bardeen-Cooper-Schrieffer (BCS) phase, is expected to be smoothly connected to the standard phase with Bose-Einstein condensation (BEC) of charged pions at μ I ≥ m π / 2 by an analytic crossover. A first hint for the existence of the BCS phase, which is likely characterised by the presence of both deconfinement and charged pion condensation, comes from the lattice observation that the deconfinement crossover smoothly penetrates into the BEC phase. To further scrutinize the existence of the BCS phase, in this article we investigate the complex spectrum of the massive Dirac operator in 2+1-flavor QCD at nonzero temperature and isospin chemical potential. The spectral density near the origin is related to the BCS gap via a generalization of the Banks-Casher relation to the case of complex Dirac eigenvalues (derived for the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential).

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