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.

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.

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).

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 Theory on Neutrino Self-Energy and Neutrino Oscillation with Consideration of Superconducting Energy Gap and Fermi’s Golden Rule

2019 ◽  
Author(s):  
Shinichi Ishiguri
Keyword(s):  
Neutrino Oscillation ◽  
Energy Gap ◽  
Transition Probabilities ◽  
Golden Rule ◽  
Neutrino Energy ◽  
Einstein Condensation ◽  
Self Energy ◽  
Superconducting Energy Gap ◽  
Bose Einstein ◽  
Many Body Interactions

We herein described an investigation of a theory, which describes the energies of neutrinos and the source of neutrino oscillations. A series of experiments were conducted to show evidences of the existence a neutrino mass. We also applied theories to explain the reason for the extremely small energy of a neutrino, mainly by employing a vacuum-derived superconducting energy gap from the Bardeen–Cooper–Schrieffer ground state. Moreover, we succeeded in obtaining the transition probabilities of neutrinos’ flavors (i.e., in terms of neutrino oscillation). We focused on the fact that up- and down-quantized space pairs combine by the Lorentz forces, undertake Bose-Einstein condensation, and then create a superconducting energy gap at the energy level of the vacuum with quantum mechanics fluctuation. Eventually, the superconducting energy gap vanishes to form a real body of the neutrino. Furthermore, assuming that the speed of the neutrino is near the speed of light and exhibits Planck’s blackbody emissions, we derived many-body interactions of neutrinos and applied them in Fermi’s golden rule. As a result, the neutrino energy we calculated agreed well within the realms of the experimental results. The calculated transition probabilities of neutrino’s flavor also explain the experiment results very well.

scholarly journals Bose–Einstein condensation in one-dimensional optical lattices: Bogoliubov’s approximation and beyond

2016 ◽  
Vol 94 (7) ◽  
pp. 697-703
Author(s):  
Mohamed K. Al-Sugheir ◽  
Mufeed A. Awawdeh ◽  
Humam B. Ghassib ◽  
Emad Alhami
Keyword(s):  
Lattice Points ◽  
Effect Of Temperature ◽  
Einstein Condensation ◽  
Condensate Fraction ◽  
Number Density ◽  
One Dimensional ◽  
Bose Einstein Condensation ◽  
Different Temperatures ◽  
Bose Einstein

Bose–Einstein condensation in a finite one-dimensional atomic Bose gas trapped in an optical lattice is studied within Bogoliubov’s approximation and then beyond this approximation, within the static fluctuation approximation. A Bose–Hubbard model is used to construct the Hamiltonian of the system. The effect of the potential strength on the condensate fraction is explored at different temperatures; so is the effect of temperature on this fraction at different potential strengths. The role of the number of lattice points (the size effect) at constant number density (the filling factor) is examined; so is the effect of the number density on the condensate fraction. The results obtained are compared to other published results wherever possible.

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.

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.

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