The Boson-Fermion model, describing a mixture of hybridized localized Bosons and itinerant Fermions on a lattice, is known to exhibit spectral properties for the Fermions which upon lowering the temperature develop into a three pole structure in the vicinity of the Fermi level. These spectral features go hand in hand with the opening of a pseudogap in the density of states upon approaching the critical temperature Tc when superconductivity sets in. In the present work we study this model, in the atomic limit where the three pole structure arises naturally from the local bonding, anti-bonding and non-bonding states between the Bosons and Fermions.
The main features of a generic boson-fermion scenario for electron pairing in a many-body correlated fermionic system are (i) a crossover from a poor metal to an insulator and finally a superconductor as the temperature decreases; (ii) the buildup of a finite amplitude of local electron pairing below a certain temperature
T∗, followed by the onset of long-range phase correlations among electron pairs below a second characteristic temperature ${T}_{\ensuremath{\varphi}};$ and (iii) the opening of a pseudogap in the density of states of the electrons below
T∗, rendering these electrons poorer and poorer quasi-particles as the temperature decreases, with the electron transport becoming ensured by electron pairs rather than by individual electrons. A number of these features have been obtained so far on the basis of different many-body techniques, all of which have their built-in shortcomings in the intermediate coupling regime, which is of interest here. In order to substantiate these features, we investigate them on the basis of an exact diagonalization study on rings up to eight sites. Particular emphasis has been put on the possibility of having persistent currents in mesoscopic rings tracking the change-over from single- to two-particle transport as the temperature decreases and the superconducting state is approached.
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.
The signature of superfluidity in bosonic systems is a sound-wave-like spectrum of the single particle excitations which in the case of strong interactions is roughly temperature independent. In Fermionic systems, where Fermion pairing arises as a resonance phenomenon between free Fermions and paired Fermionic states (examples are: the atomic gases of
6Li or
40K controlled by a Feshbach resonance, polaronic systems in the intermediary coupling regime,
d-wave hole pairing in the strongly correlated Hubbard system), remnants of such superfluid characteristics are expected to be visible in the normal state. The single particle excitations maintain a sound-wave-like structure for wave vectors above a certain
qmin(T) where they practically coincide there with the spectrum of the superfluid phase for
T<Tc. Upon approaching the transition from above this region in
q space extends down to small momenta, except for a narrow region around
q=0 where such modes change into damped free particle like excitations.
The boson-fermion model, describing a mixture of itinerant electrons hybridizing with tightly bound electron pairs represented as hardcore bosons, is here generalized with the inclusion of a term describing on-site Coulomb repulsion between fermions with opposite spins. Within the general framework of the dynamical mean-field theory, it is shown that around the symmetric limit of the model this interaction strongly competes with the local boson-fermion exchange mechanism, smoothly driving the system from a pseudogap phase with poor conducting properties to a metallic regime characterized by a substantial reduction of the fermionic density. On the other hand, if one starts from correlated fermions described in terms of the one-band Hubbard model, the introduction in the half-filled insulating phase of a coupling with hardcore bosons leads to the disappearance of the correlation gap, with a consequent smooth crossover to a metallic state.
The spectral properties of a mixture of bosons hybridized with fermion pairs are studied in the superconducting state. Such a model exhibits two limiting behaviors. One is reminiscent of a BCS system, provided that the total concentration n of particles is below a certain critical concentration
nc, in which case bosons exist only in thermally excited states. The other limit for n\ensuremath{\geqslant}
nc describes a situation largely controlled by the condensation of the bosons. The variation of the single-boson as well as collective excitations as a function of n and for the entire temperature regime from T=0 K to
Tc will be discussed, both with and without long-range Coulomb interaction between the charge carriers. The method for calculation applied here is based on the dielectric formalism and the use of Ward identities, currently used in the theory of the interacting Bose gas, which allows us to derive the density and current correlation functions consistent with local charge-current conservation laws. In the absence of a Coulomb interaction the behavior of the system is characterized by the existence of a sound-wave-like branch in the Bose single-particle and collective excitation spectrum. In the BCS regime the sound velocity is proportional to the Fermi velocity while in the Bose regime it is proportional to the strength of the boson-fermion hybridization and decreases with the superfluid density as we approach
Tc. In the presence of a long-range Coulomb interaction and in the Bose regime one observes, besides the usual optical plasmon mode at high frequency and corresponding to in-phase density oscillation of the two subsytems, an out-of-phase collective mode in the two particle continuum just above the gap. Moreover, upon approaching
Tc a relatively well-defined quasiparticle feature starts to emerge within the gap and is seen in both the Bose single-particle excitation and the density oscillation spectrum. In the BCS regime, due to the very small number of occupied bosonic states, the low-energy quasiparticle features are absent. \textcopyright{} 1996 The American Physical Society.