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International Journal of Modern Physics B

LOWERING OF BOSON-FERMION SYSTEM ENERGY WITH A GAPPED COOPER RESONANT-PAIR DISPERSION RELATION

T. A. Mamedov, MANUEL DE LLANO

Published May 30, 2007• 8 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979207043701

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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.
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.
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.
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{T}_{c}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 reveal a quantum coherent state characterized by composite bosonic trions, wherein paired fermions further bind with bosons, in one-dimensional Bose-Fermi mixtures.This phase emerges in two separate models, both featuring onsite boson-fermion attraction that induces negative binding energy for the composite trions. The first is the pair-hopping model, in which spinless fermions undergo pair hopping to form preformed pairs. The second is the extended Bose-Fermi Hubbard model, describing dipolar bosons and fermions with density-density interactions. Notably, the formation of composite trions is independent of the specific pairing interactions of fermions. Extensive density matrix renormalization group calculations demonstrate the quasi-condensation of the composite trions, evidenced by algebraically decaying correlations of trions, gapped single-particle excitations, and suppressed fermion pair correlations. Our findings provide valuable insights into the three-body pairing mechanism in mixed-particle systems.