The two component model of coexisting local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems, is discussed. The cases of isotropic s-wave and anisotropic pairing of extended s and d x 2 −y 2-wave symmetries are analyzed for a 2D square lattice within the BCS-mean field approximation and the Kosterlitz-Thouless theory. We determined the phase diagrams and superconducting characteristics as a function of the position of the local pair (LP) level and the total electron concentration. The model exhibits several types of interesting crossovers from BCS like behavior to that of LP’s. Some of our results are discussed in connection with a two-component scenario of preformed pairs and unpaired electrons for exotic superconductors. Key words: Boson-Fermion model, Phase fluctuations A system of interacting charged bosons (bound electron pairs) and electrons can show features which are intermediate between those of local pair superconductors and those of classical BCS systems. Such a two component (bosonfermion) model is of relevance for high temperature superconductors (HTS) and other exotic superconductors [1,2,3,4,5,6,7,8,9,10]. Recently, we have studied a generalization of this model to the case of anisotropic pairing [9,10]. Here, we shortly outline the study and present further results concerning the phase diagrams and superconducting properties of such a system in the case of isotropic s-wave pairing as well as for anisotropic pairings of d- and extended s-wave symmetries, for a 2D square lattice.
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.
The superconducting properties of the 2D fermion system with local and different types of the indirect boson-exchange attractions in the cases of s-wave and d-wave pairing are reviewed and analysed at T=0. In particular, the possibility of the crossover from the Bose-Einstein condensation regime to the BCS-like superconductivity with the carrier density and coupling changing in the case of different pairing channels is discussed. Gaussian fluctuations of the order parameter are taken into account and the carrier density dependence of the gap is studied in this case. The role of the interaction form in the physical behavior of the systems is also discussed.
We investigate the two-dimensional attractive Hubbard model with quantum Monte Carlo techniques to reveal the crossover from a BCS-type superconductivity in the weak-coupling regime to a superconductivity properly described by a Bose-Einstein condensation (BEC) of local, preformed pairs. The crossover from BCS to BEC is particularly well exposed in the temperature dependence of both the spin susceptibility and the double occupancy, as well as by the appearance of a pseudogap in the density of states far above
Tc. These features are also mirrored in the shape of the specific-heat peak around
Tc, the separation of the temperature regimes where pair formation and their condensation occur, and in the transfer of spectral weight from the single-particle excitation branch to a pair band in the normal state. \textcopyright{} 1996 The American Physical Society.
In this paper we address the behavior of the superfluid transition temperature
Tc in the attractive Hubbard model. The attractive Hubbard model can be regarded as the generalization of the BCS to Bose-Einstein condensation (BEC) crossover to a lattice and, as such, may have implications for future optical lattice studies. Nevertheless, the BEC limit of the Hubbard model is very different from that of the better-studied Fermi gases, owing to the strong intersite repulsion between pairs. Here we address systematically the effects of pairing fluctuations for all filling fractions over the entire range of attractive interaction strength. A central conclusion of our work is that in a lattice, around half filling, the smooth evolution from the BCS to the BEC limits is interrupted:
Tc vanishes when the system approaches the bosonic regime with increasing interaction strength. We suggest that this interruption of crossover may signal a quantum critical transition to another form of superfluid not continuously connected to a BCS-like phase. A simple variational ansatz for an alternate ground state in this more strongly coupled superfluid is presented. A generalization of the (
s-wave) Hubbard model to
d-wave pairing allows us to address issues of relevance to high-
Tc superconductivity. The phase diagram (representing the pairing or pseudogap onset temperature
T∗ and
Tc) shows that here too one observes a vanishing of
Tc when
T∗ becomes sufficiently large. Given this predicted breakdown of the crossover, and given the striking similarity to features of the cuprate phase diagram, we suggest that future experiments on ultracold fermions in optical lattices should not be exclusively limited to the repulsive Hubbard model, but should address the attractive model in order to elucidate features of high-temperature superconductivity.
We study a generalized periodic Anderson model with on-site hybridization between wide- and narrow-band electrons and strong and local coupling with the lattice deformation. Provided that the interaction with the lattice is strong enough, the narrow-band electrons will be turned into small polarons which interact attractively with each other over short distances, leading to the formation of local pairs of narrow-band electrons. This leads to a pinning of the Fermi level which is due to the fact that narrow-band electrons exist only in pair states. By means of a generalized Schrieffer-Wolff transformation we eliminate hybridization and obtain an effective Hamiltonian which describes a contact interaction between local pairs and wide-band electrons as well as the direct hopping of local pairs and interparticle Coulomb interactions. In such a system the two types of mechanisms which can lead to superconductivity have been studied. The first one is due to direct local pair hopping and involves exclusively the narrow-band subsystem giving rise to a superconductivity analogous to superfluidity in
4He. The second one is due to a contact interaction between local pairs and pairs of wide-band electrons. This leads to a superconducting state involving both subsystems where the local pairs of the narrow-band subsystem induce Cooper pairing amongst the electrons of the wide-band subsystem. Consequently, the single-particle spectrum of the wide-band electrons opens up a gap around the position of the narrow band of electrons in pair states.We study the phase diagrams and the superconducting properties of two such coupled subsystems involving bosons and fermions as a function of the position of the narrow band with respect to the wide band (or the relative concentration of narrow and wide-band electrons). We also show that the critical temperature
Tc and
Tc/
Eg(0) [
Eg(0) being the energy gap] follow, in general, a strong and nonmonotonic variation. One of the most striking features of this system is that the pairs of narrow-band electrons exist in the normal phase and condense on approaching
Tc from above. The existence of such a narrow boson band together with a fermion band in the normal phase leads to characteristic behavior in the specific heat over temperature variation being very similar to that observed in recent studies of nonclassical superconductors.