M. Casas, Antonio Puente, A. Rigó, M. J. DAVIDSON, R. M. Quick, Mauricio Fortes, M. A. Solís, MANUEL DE LLANO, Oracio Navarro, Ariel A. Valladares, O. Rojo
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.
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.
Unification of the Bardeen, Cooper and Schrieffer (BCS) and the Bose‐Einstein condensation (BEC) theories is surveyed in terms of a generalized BEC (GBEC) finite‐temperature statistical formalism. A vital distinction is that Cooper pairs (CPs) are true bosons that may suffer a BEC since they obey BE statistics, in contrast with BCS pairs that are “hard‐core bosons” at best. A second crucial ingredient is the explicit presence of hole‐pairs (2h) alongside the usual electron‐pairs (2e). A third critical element (particularly in 2D where ordinary BEC does not occur) is the linear dispersion relation of CPs in leading order in the center‐of‐mass momentum (CMM) power‐series expansion of the CP energy. The GBEC theory reduces in limiting cases to all five continuum (as opposed to “spin”) statistical theories of superconductivity, from BCS on one extreme to the BEC theory on the other, as well as to the BCS‐Bose “crossover” picture and the 1989 Friedberg‐Lee BEC theory. It accounts for 2e‐ and 2h‐CPs in arbitrary proportions while BCS theory can be deduced from the GBEC theory but allows only equal (50%‐50%) BE condensed‐mixtures of both kinds of CPs. As it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero‐temperature condensation energy for all couplings, it suggests that the BCS condensate is a BE condensate of a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly‐bound zero‐CMM 2e‐ and 2h‐CPs. Without abandoning the electron‐phonon mechanism in moderately weak coupling, and fortuituously insensitive to the BF interactions, the GBEC theory suffices to reproduce the unusually high values of Tc (in units of the Fermi temperature TF) of 0.01–0.05 empirically found 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.
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.
Boson-Fermion models of superconductivity are getting attention as they are able to explain some of the high temperature superconductor's properties. Here we report on the condensation energy of a 3D non-interacting mixture of paired fermions (electrons) as Cooper pairs assumed to be composite bosons, which are responsible for carrying superconductivity, plus unpaired fermions both trapped in a periodic multilayer structure like that of the cuasi-two dimensional High-Temperature superconductor planes, generated by applying an external Dirac's comb potential in the direction perpendicular to the planes where superconductivity preferably occurs, while in the other two directions parallel to the planes the mixture moves freely. For bosons we give the Bose-Einstein condensation critical temperature, which we assume is equal to the superconducting critical one, while for both bosons and fermions we give the chemical potential, the internal energy and the entropy, all of them as functions of temperature, in order to calculate the Helmholtz free energy, which we use to obtain the condensation energy of a mixture of NF ideal fermions (electrons), which after turning on the attractive pair interaction become NB=NF/2 ideal bosons. For several plane impenetrability magnitudes, we calculate the condensation energy as the difference between the free energies of the fermions which are in the normal state minus that of the bosons in the condensed state, where we observe that as the plane impenetrability increases: the condensation energy increases; the critical temperature decreases, as expected for example for cuprate superconductors, and the behavior of the entropy and the internal energy show a dimensional crossover from 3D to 2D.
Abstract The superfluid density ns(T) n s ( T ) of a superconductor is calculated based on the generalized Bose–Einstein condensation (GBEC) theory that addresses a fully-interacting ternary boson-fermion gas mixture of free electrons as fermions, plus two-electron Cooper pairs (2eCPs) and also, explicitly, two-hole Cooper pairs (2hCPs), both as bosons. Here we consider two special cases (i) 100%–0% (i.e., with no condensed 2hCPs) and (ii) 0%–100% (i.e., with no condensed 2eCPs). Subsumed in GBEC are the Bardeen–Cooper–Schrieffer (BCS) and Bose–Einstein condensation (BEC) theories along with the BCS-BEC crossover theory extended with 2hCPs. We find that in the weak-coupling regime ns(0) n s ( 0 ) agrees with data from the Uemura et al. (2004) graph for several elemental SCs by taking in 3D with a quadratic energy-dispersion relation while in 2D with a linear relation are much too far below the data. In the strong-coupling regime the linear behavior of critical temperature Tc T c vs ns(0) n s ( 0 ) obtained here is just as Božović et al. (2016) found. However, in 2D with a linear relation accounting for 0%–100%, ns(T)/ns(0) n s ( T ) / n s ( 0 ) compares well with some high- Tc T c -cuprate SC data between the two coupling regimes.
A two component model of negative U centers coupled with the Fermi sea of itinerant fermions is discussed in connection with high-temperature superconductivity of cuprates, and superfluidity of atomic fermions. We examine the phase transition and the condensed state of this boson-fermion model (BFM) beyond the ordinary mean-field approximation in two and three dimensions. No pairing of fermions and no condensation are found in two-dimensions for any symmetry of the order parameter. The expansion in the strength of the order parameter near the transition yields no linear homogeneous term in the Ginzburg-Landau-Gor'kov equation and a zero upper critical field in any-dimensional BFM, which indicates that previous mean-field discussions of the model are flawed. Normal and anomalous Green's functions are obtained diagrammatically and analytically in the condensed state of a simplest version of 3D BFM. A pairing of bosons analogous to the Cooper pairing of fermions is found. There are three coupled condensates in the model, described by the off-diagonal single-particle boson, pair-fermion and pair-boson fields. These results negate the common wisdom that the boson-fermion model is adequately described by the BCS theory at weak coupling.
Various BCS-like pairing theories are still invariably used to describe the unusual superconducting/superfluid states and properties of condensed matters without clarifying the fermionic or bosonic nature of Cooper pairs and the relevant mechanisms of superconductivity and superfluidity. We show that the bosonization of Cooper pairs and the novel superconductivity and superfluidity resulting from the condensation of an attractive Bose gas of Cooper pairs into a superfluid state in high-Tc cuprates and other exotic systems occur under the condition εF≲2εA (where εF is the Fermi energy, εA is the energy of the effective attraction between fermions). We argue that the simple BCS criterion (i.e. formation of an energy gap on the Fermi surface) is insufficient for the occurrence of unconventional superconductivity (superfluidity) and the superconducting/superfluid transition in attractive Bose systems is more λ-like than the usual Bose–Einstein condensation. The new and specific criteria for unconventional superconductivity and superfluidity are formulated. Mean-field theory of the three- and two-dimensional superfluid Bose condensates of Cooper pairs describes reasonably well the novel superconducting states (i.e., two distinct superconducting phases below the bulk superconducting transition temperature Tc and a vortex-like state above Tc) and properties (such as λ-like transition at Tc, first-order phase transition and gapless bosonic excitations somewhat below Tc or even far below Tc) of high-Tc cuprates in full agreement with the experimental findings. The unusual superconducting/superfluid states and properties of heavy-fermion and organic compounds, Sr2RuO4, 3He, 4He and atomic Fermi gases are explained more clearly by this theory.