Bose-Einstein condensation with a BCS model interaction

Casas, M.; Rigó, A.; Llano, M. de; Rojo, O.; Solís, M. A.

doi:10.1016/s0375-9601(98)00377-6

Cited by 36 publications

(39 citation statements)

References 48 publications

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“…Recent experimental studies of the spectral intensity of photoelectron emission in high T c cuprate superconductors have provided evidence that bound electron Cooper pairs (pairons) already exist at temperatures higher than the critical transition temperature [1]. This finding is consistent with several theoretical proposals that suggest that high T c superconductivity (HTSC) originates from a 2D Bose-Einstein condensate (BEC) of pairons pre-existing above T c , coupled through a BCS-like phonon mechanism [2,3]. The 2D character of the phase transition is associated with the layered structure of cuprates, which in the case of YBaCu 3 O 7−y (YBCO) consists of a succession of layers along the c-axis with a unit cell of length c ≈ 12Å, and the chemical composition CuO-BaO-CuO 2 -Y-CuO 2 -BaO-CuO.…”

supporting

confidence: 78%

“…Accordingly, we describe the total amount of charge carriers by means of an ideal mixture of non-interacting unpaired fermions, and breakable pairons with a linear dispersion relation [3,10]. The fermion number per unit area is n f = n f 1 + n f 2 , where n f 1 and n f 2 denote the number densities of unpairable, and pairable fermions, respectively.…”

mentioning

confidence: 99%

“…By asserting that in thermal equilibrium this kind of fermions arises precisely from broken pairons [3], we identify n…”

mentioning

confidence: 99%

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BOSE-EINSTEIN CONDENSATION IN QUASI-2D SYSTEMS: APPLICATIONS TO HIGH-T_c SUPERCONDUCTIVITY

Villarreal

Llano

2010

Quantum Field Theory Under the Influence of External Conditions (QFEXT09)

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We calculate the number and energy densities of a quasi-2D Bose-Einstein gas constrained within a thin region of infinite extent but of finite width δ. The BEC critical transition temperature then becomes an explicit function of δ. We use this result to construct a model of high-Tc superconductivity in cuprates with a periodic layered atomic structure. The predicted behavior of the BEC Tc agrees with recent experimental findings in severely underdoped cuprates.

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confidence: 78%

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confidence: 99%

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BOSE-EINSTEIN CONDENSATION IN QUASI-2D SYSTEMS: APPLICATIONS TO HIGH-T_c SUPERCONDUCTIVITY

Villarreal

Llano

2010

Quantum Field Theory Under the Influence of External Conditions (QFEXT09)

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“…Expressions more general than (2) and (3) but reducing to them, are known [20] in any dimensionality d > 0 (integer or not) and for any dispersion relation…”

Section: Bose-einstein Condensationmentioning

confidence: 99%

Further Evidence for Linearly-Dispersive Cooper Pairs

Llano

Valencia

2006

Mod. Phys. Lett. B

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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 vs. temperature formula poorly fits penetration-depth data for two cuprates in the range 1/2 < T /T c ≤ 1 where T c is the BEC transition temperature. We show how these fits are dramatically improved assuming cuprates to be quasi-2D, and how equally good fits obtain 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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“…Unfortunately, both sets of predictions are well below empirical cuprate values of T c /T F varying [40] from 0.03−0.09. Pure gas model results [31] for either breakable or unbreakable bosons without unpaired fermions are seen in the figure to overestimate empirical T c /T F values by factors ranging from two to more than two orders of magnitude. All these results are wide off the mark.…”

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Two-dimensional Bose-Einstein condensation in cuprate superconductors

Casas¹,

Llano²,

Puente³

et al. 2002

Solid State Communications

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Transition temperatures Tc calculated using the BCS model electron-phonon interaction without any adjustable parameters agree with empirical values for quasi-2D cuprate superconductors. They follow from a two-dimensional gas of temperaturedependent Cooper pairs in chemical and thermal equilibrium with unpaired fermions in a boson-fermion (BF) statistical model as the Bose-Einstein condensation (BEC) singularity temperature is approached from above. The linear (as opposed to quadratic) boson dispersion relation due to the Fermi sea yields substantially higher Tc's with the BF model than with BCS or pure-boson BEC theories.PACS Mott [7] and their co-workers. But BEC normally occurs only for dimensions d > 2 while some modern superconductors are quasi-2D or even quasi-1D materials. We show, however, that CPs can undergo BEC for all d > 1. We further obtain reasonable critical temperatures T c without any adjustable parameters, thus bolstering the above mentioned conjecture even before building in full many-body self-consistency. As in BCS theory, fluctuations have also been neglected. More detailed, sophisticated treatments actually link [8][9][10][11][12]. BEC (characterized by a bosonic condensate fraction) with the BCS theory (characterized by a fermionic gap), but report no attempts to calculate specific T c 's without adjustable parameters to compare with experiment.A BEC picture of superconductivity is consistent with the recent discovery of the "pseudogap" in the electronic density of states [13][14][15][16][17][18][19] above T c in certain cuprates, at least with one of its major interpretations as "pre-formed CPs" without long-range coherence or condensation, while in BCS theory CP formation and condensation occur simultaneously below the same T c . We here submit that a natural candidate for such pre-formed CPs are the nonzero-center-of-mass CPs usually neglected in BCS theory.To fix the dynamics take a 2D system of N fermions of mass m confined in a square of area L 2 interacting pairwise via the BCS model electron-phonon interaction V k,k ′ = −V , with V > 0, whenever µ(T )−hω D < ǫ k1 (≡h 2 k 2 1 /2m), ǫ k2 < µ(T )+hω D , and zero otherwise, where k ≡ 1 2 (k 1 − k 2 ) is the relative wavevector of the two particles; µ(T ) the ideal Fermi gas (IFG) chemical potential, which at T = 0 becomes the Fermi energy E F ≡h 2 k 2 F /2m with k F the Fermi wavenumber; and ω D the Debye frequency. Striking direct evidence for significant electron-phonon coupling in hightemperature cuprate superconductors from angle-resolved photoemission spectroscopy (ARPES) experiments has recently been reported [20].IfhK =h(k 1 + k 2 ) is the center-of-mass momentum (CMM) of a CP, let E K be its total energy 1

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Bose-Einstein condensation with a BCS model interaction

Cited by 36 publications

References 48 publications

BOSE-EINSTEIN CONDENSATION IN QUASI-2D SYSTEMS: APPLICATIONS TO HIGH-T_c SUPERCONDUCTIVITY

BOSE-EINSTEIN CONDENSATION IN QUASI-2D SYSTEMS: APPLICATIONS TO HIGH-T_c SUPERCONDUCTIVITY

Further Evidence for Linearly-Dispersive Cooper Pairs

Two-dimensional Bose-Einstein condensation in cuprate superconductors

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Bose-Einstein condensation with a BCS model interaction

Cited by 36 publications

References 48 publications

BOSE-EINSTEIN CONDENSATION IN QUASI-2D SYSTEMS: APPLICATIONS TO HIGH-Tc SUPERCONDUCTIVITY

BOSE-EINSTEIN CONDENSATION IN QUASI-2D SYSTEMS: APPLICATIONS TO HIGH-Tc SUPERCONDUCTIVITY

Further Evidence for Linearly-Dispersive Cooper Pairs

Two-dimensional Bose-Einstein condensation in cuprate superconductors

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Product

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BOSE-EINSTEIN CONDENSATION IN QUASI-2D SYSTEMS: APPLICATIONS TO HIGH-T_c SUPERCONDUCTIVITY

BOSE-EINSTEIN CONDENSATION IN QUASI-2D SYSTEMS: APPLICATIONS TO HIGH-T_c SUPERCONDUCTIVITY