The properties of a mixture of mutually interacting bound electron pairs and itinerant fermions (the boson-fermion model) on a lattice are further studied. We determine the superconducting critical temperature from a pseudogap phase by applying a self-consistent
T-matrix approach, which includes the pairing fluctuations and the boson self-energy effects. The analysis is made for a three dimensional cubic lattice with tight-binding dispersion for electrons and for both standard bosons and the case of hard-core bosons. The results describe the BCS-Bose-Einstein condensation crossover with varying position of the bosonic (local pair) level and give a further insight into the nature of resonance superfluidity in the boson-fermion model.
By means of the functional-integral formulation we discuss the occurrence of superconductivity resulting from Bose-Einstein condensation within a model describing preformed pairs which coexist in thermal equilibrium with unpaired fermions. At saddle-point level we study the thermodynamic properties of the model as functions of the boson excitation energy $\ensuremath{\nu},$ discussing the results in connection with the phenomenology of the pseudogap state of the superconducting cuprates. For temperatures above the Bose-Einstein condensation temperature
Tc we also analyze the effects of Gaussian fluctuations on the critical temperature and on the boson spectrum. Finally, we compare the bosonic effective action which controls thermal fluctuations of the mixture to the time-dependent Ginzburg-Landau functional of an interacting fermionic system at intermediate coupling.
We analyze the ground-state properties of mixtures consisting of scalar bosons and spin-
21 fermions using a mean-field treatment of the local boson-fermion interaction on a simple cubic lattice. In the deep superfluid limit of the boson sector and the BCS regime of the fermion sector, we derive BCS-type equations to determine the phase diagram of the system. We find a competition between a charge density wave and a superconducting phase. In the opposite limit, we study the Mott-insulator-to-superfluid transition of the boson sector in the presence of a staggered density-induced alternating potential provided by the fermions, and determine the mean-field transition line. In the two-superfluids phase of the mixture, we restrict to nearest-neighbor-induced interactions between the fermions and consider the extended Hubbard model. We perform a mean-field analysis of the critical temperature for the formation of boson-assisted
s-, extended ${s}^{\ensuremath{-}}$-,
d-, and
p-wave pairs at fermionic half-filling. We compare our results with a recent dynamical mean-field study [P. Anders et al., Phys. Rev. Lett. 109, 206401 (2012)].
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.
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
s-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
T, 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∗ and Bose-Einstein condensation
Tc temperatures in terms of $\ensuremath{\mu}(\ensuremath{\lambda},T)$ and $2\ensuremath{\Delta}(\ensuremath{\lambda})$. In particular, even at the
s-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 vs doping behavior both of which hinge on the gapped boson spectrum.
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.