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The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics

Depairing and Bose–Einstein condensation temperatures in a boson–fermion superconductor model with Coulomb effects

T. A. Mamedov, MANUEL DE LLANO

Published Apr 30, 2013• 11 citations
Publisher

Abstract

An extended boson–fermion (BF) model is introduced describing the evolution of attractively interacting single electrons into a binary mixture of unpaired electrons plus incoherent bosonic Cooper pairs as absolute temperature is lowered. The new model is employed to determine how the system, upon cooling, exhibits critical temperatures for: a) incoherent boson formation below as well as b) for creating a coherent boson fluid below . Critical temperatures and are related with the dynamical parameters of the attractively interacting fermion system. It is shown that the introduction of a uniform Coulomb interaction in an anisotropic BF binary gas mixture model allows finding not only a self-consistent description of a pseudogap and a dome-shaped -vs-doping behaviour, but also to predict, even in a phonon-mediated many-electron dynamics, of an energy–momentum dispersion that is either gapped or not depending on direction. This manifests itself in high- superconductors as curves in momentum space along which the superconducting gap vanishes, hence giving rise to the so-called “Fermi arcs” observed in angle-resolved-photoemission spectroscopy experiments.

DOI
10.1080/14786435.2013.790568

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On the Boson–Fermion resonant model on a lattice

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We review briefly the properties of a mixture of mutually interacting bosons (bound electron pairs) and itinerant fermions on a lattice (the boson–fermion model). The calculations of the superconducting phase transition temperature () and the phase diagram are the main concern. The self-consistent -matrix method is applied to determine the superconducting critical temperature from a pseudogap phase. The method takes into account the pairing fluctuations effects. The -matrix results for are given for a three-dimensional (3-D) cubic lattice with tight-binding dispersion of electrons and standard bosons, and they are also compared with those of the BCS- mean-field approximation. Our results describe the BCS-Bose-Einstein condensation crossover in the boson–fermion mixture with resonant interaction. The energy scales involved in the pseudogap formation are also analysed.

arXiv:1912.04094•The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics•Nov 21, 2014•4 citations
An extended boson–fermion (BF) model is introduced describing the evolution of attractively interacting single electrons into a binary mixture of unpaired electrons plus incoherent bosonic Cooper pairs as absolute temperature is lowered. The new model is employed to determine how the system, upon cooling, exhibits critical temperatures for: a) incoherent boson formation below as well as b) for creating a coherent boson fluid below . Critical temperatures and are related with the dynamical parameters of the attractively interacting fermion system. It is shown that the introduction of a uniform Coulomb interaction in an anisotropic BF binary gas mixture model allows finding not only a self-consistent description of a pseudogap and a dome-shaped -vs-doping behaviour, but also to predict, even in a phonon-mediated many-electron dynamics, of an energy–momentum dispersion that is either gapped or not depending on direction. This manifests itself in high- superconductors as curves in momentum space along which the superconducting gap vanishes, hence giving rise to the so-called “Fermi arcs” observed in angle-resolved-photoemission spectroscopy experiments.
A boson–fermion (BF) quantum-statistical binary gas mixture model of high- T c superconductors (HTSCs) recently introduced consists of resonant bosonic Cooper electron pairs (CPs) in chemical and thermal equilibrium with single unpaired electrons. Here, this model is refined and extended to include: i) the anisotropy of the original BF vertex interaction causing boson formation/disintegration and ii) momentum-independent Coulomb repulsions between electron charge carriers. It is shown that pair breakings due to Coulomb repulsion depend on the separation between boson and fermion spectra. Specifically, as such a separation shrinks, the pair-breaking ability of the Coulomb interaction weakens and disappears altogether at the Bose–Einstein condensation (BEC) T c , i.e., at the temperature at which a complete softening of bosons occurs due to boson self-energy renormalization. Simultaneous inclusion of both effects produces “islands” in momentum space of incoherent CPs above the Fermi sea as temperature is lowered. These islands grow upon further cooling and merge together just before T c is reached. The BF model thusly extended now predicts a pseudogap phase in 2D HTSCs with lines of points on the Fermi surface along which the pseudogap vanishes, hence explaining the origin of the temperature-dependent “Fermi arcs” observed in experiments.
Starting from the Friedberg-TD Lee Hamiltonian describing a coexisting and dynamically interacting many-particle binary boson-fermion gas mixture with a coupling $(\ensuremath{\lambda})$-dependent gap $2\ensuremath{\Delta}(\ensuremath{\lambda})$ in the boson dispersion relation for the sss-wave Cooper or BCS model interaction, we deduce several observed characteristic features of high-temperature superconductors at the simplest level. Analytic expressions for both the unpaired-fermion and boson number densities, as well for the fermion chemical potential $\ensuremath{\mu}(\ensuremath{\lambda},T)$, all of which vary with the degree of bosonization and with temperature TTT, are derived in detail using two-time, finite-temperature Green function techniques. Simple implicit formulas are then obtained for both two and three dimensions for the pseudogap T∗{T}^{*}T∗ and Bose-Einstein condensation Tc{T}_{c}Tc​ temperatures in terms of $\ensuremath{\mu}(\ensuremath{\lambda},T)$ and $2\ensuremath{\Delta}(\ensuremath{\lambda})$. In particular, even at the sss-wave level we find a self-consistent description of the generic phase diagram observed in cuprates, including the appearance of a pseudogap and a dome-shaped Tc{T}_{c}Tc​ vs doping behavior both of which hinge on the gapped boson spectrum.
A recent boson-fermion (BF) binary gas mixture model is extended to include: (i) anisotropy of the BF interaction and (ii) momentum-independent Coulomb repulsions. It is applied to account for the peculiarities of the pseudogap observed as function of absolute temperature T and concentration x of holes doped onto the CuO 2 planes and to study the further transformation of the pseudogap into the real superconducting gap, as T is lowered. Using two-time Green functions it is shown that pair breakings depend on the separation between the boson and fermion spectra of the BF mixture. As this separation shrinks, the pair-breaking ability of the Coulomb interaction weakens and disappears at the BEC T c , i.e., at the T below which a complete softening of bosons occurs. Simultaneous inclusion of both effects (i) and (ii) produces, as T is lowered, "islands" in momentum space of incoherent Cooper pairs above the Fermi sea. These islands grow upon further cooling and merge together just before T c is reached. The new extended BF model predicts a pseudogap phase in 2D high-T c superconductors with lines of points, or loci, on the Fermi surface along which the pseudogap vanishes. This explains the origin of T-dependent "Fermi arcs" observed in ARPES experiments.
In a nearly‐filled energy band where scattering of electrons is hampered, a pairing interaction between two electrons and quanta in a solid (e.g., phonons or spin‐resonances or some other excitation of electronic origin) can still occur in the s‐channel where a field quantum mediates the coalescence of two fermions into a new composite particle. By describing the attractively‐interacting electrons as a gas mixture of individual electrons plus bosons made up of two electrons, the dependence on momentum of the energy of single electrons is investigated. When the net interaction BCS dimensionless coupling constant λ and the ratio with the maximum energy of a quantum mediating the pairing to the Fermi energy increases, the coalescence of electrons at temperatures higher than the Bose–Einstein condensation (BEC) temperature of bosons leads to the appearance of steep (waterfall‐like) changes in the high‐energy electron spectrum of the binary boson–fermion (BF) gas mixture. These waterfall‐like anomalies seen in high‐ superconductors (HTSCs) are in fact a characteristic property of a BF gas mixture and reflect the splitting of the conduction band into two subbands emerging as the number of two‐electron bosons increases.
Applying two-time Green-function techniques to the Friedberg-T.D. Lee phenomenological Hamiltonian of a many-fermion system, it is shown that positive-energy resonant bosonic pairs associated with four-fermion excitations above the Fermi sea are energetically lower in a ground-state that is a mixture of two coexisting and dynamically interacting many-particle subsystems: a) unpaired fermions and b) composite bosons. It is argued that an interaction between free fermions and bosons excited above the Fermi sea in the mixture, namely, the continuous processes of pair-formation from, and disintegration into, two unpaired electrons, results in a substantially lowering the total system energy. The positive-energy composite bosons begin to appear incoherently below a depairing temperature T* as their coupling- and temperature-dependent number density gradually increases from zero. This leads quite naturally to the pseudogap phenomenon observed in high-Tccuprates.
We review briefly the properties of a mixture of mutually interacting bosons (bound electron pairs) and itinerant fermions on a lattice (the boson–fermion model). The calculations of the superconducting phase transition temperature () and the phase diagram are the main concern. The self-consistent -matrix method is applied to determine the superconducting critical temperature from a pseudogap phase. The method takes into account the pairing fluctuations effects. The -matrix results for are given for a three-dimensional (3-D) cubic lattice with tight-binding dispersion of electrons and standard bosons, and they are also compared with those of the BCS- mean-field approximation. Our results describe the BCS-Bose-Einstein condensation crossover in the boson–fermion mixture with resonant interaction. The energy scales involved in the pseudogap formation are also analysed.