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arXiv:cond-mat/0210057 · Physical review. B, Condensed matter

Superconductivity with hard-core repulsion: BCS-Bose crossover and s−/d -wave competition

F. Pistolesi, Ph. Nozières

Published Aug 1, 2002• 14 citations
arXivHTMLPDF

Abstract

We consider fermions on a two-dimensional lattice interacting repulsively on the same site and attractively on the nearest-neighbor sites. The model is relevant, for instance, to study the competition between antiferromagnetism and superconductivity in a Kondo lattice. We first solve the two-body problem to show that in the dilute and strong-coupling limit the s-wave Bose condensed state is always the ground state. We then consider the many-body problem and treat it at mean-field level by solving exactly the usual gap equation. This guarantees that the superconducting wave function correctly vanishes when the two fermions (with antiparallel spin) sit on the same site. This fact has important consequences for the superconducting state that are somewhat unusual. In particular this implies a radial node line for the gap function. When a next-neighbor hopping ${t}^{\ensuremath{'}}$ is present we find that the s-wave state may develop nodes on the Fermi surface.

DOI
10.1103/physrevb.66.054501

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We consider fermions on a two-dimensional lattice interacting repulsively on the same site and attractively on the nearest-neighbor sites. The model is relevant, for instance, to study the competition between antiferromagnetism and superconductivity in a Kondo lattice. We first solve the two-body problem to show that in the dilute and strong-coupling limit the s-wave Bose condensed state is always the ground state. We then consider the many-body problem and treat it at mean-field level by solving exactly the usual gap equation. This guarantees that the superconducting wave function correctly vanishes when the two fermions (with antiparallel spin) sit on the same site. This fact has important consequences for the superconducting state that are somewhat unusual. In particular this implies a radial node line for the gap function. When a next-neighbor hopping t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ is present we find that the s-wave state may develop nodes on the Fermi surface.
Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange (JJJ) and correlated hopping (KKK) interaction. Detailed numerical analysis of sss-, ppp-, and ddd-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (ttt) and next-nearest- (t2{t}_{2}t2​) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the ddd-wave and the extended sss-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the t2t\frac{{t}_{2}}{t}tt2​​ ratio, giving in particular for t2=0{t}_{2}=0t2​=0 sss-wave (ddd-wave) pairing as most favorable in the low (high) density limit, but increasing t2{t}_{2}t2​ can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects sss-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.
We considered the BCS-BEC crossover at T = 0 in the framework of a lattice fermion model (the extended Hubbard model).We analyzed the case of on-site hard core repulsion (U = ∞) and intersite attraction (W < 0) in a 3D system with extended s-wave pairing symmetry.The mechanisms of density-driven and attraction-strength-driven crossover were analyzed.We obtained the ground state phase diagram.The analyzed quantities are: chemical potential, order parameter, coherence length, and fraction of condensed particles.
The t-J model is believed to be a minimal model that may be capable of describing the low-energy physics of the cuprate superconductors. However, although the t-J model is simple in appearance, obtaining a detailed understanding of its phase diagram has proved to be challenging. We are therefore motivated to study modifications to the t-J model such that its phase diagram and mechanism for d-wave superconductivity can be understood analytically without making uncontrolled approximations. The modified model we consider is a t’- J_z J z -V model on a square lattice, which has a second-nearest-neighbor hopping t’ (instead of a nearest-neighbor hopping t, an Ising (instead of Heisenberg) antiferromagnetic coupling J_z J z , and a nearest-neighbor repulsion V. In a certain strongly interacting limit, the ground state is an antiferromagnetic superconductor that can be described exactly by a Hamiltonian where the only interaction is a nearest-neighbor attraction. BCS theory can then be applied with arbitrary analytical control, from which nodeless d-wave or s-wave superconductivity can result.
In this work we use functional integral techniques to examine the nearest-neighbor attractive Hubbard model on a quasi-two-dimensional lattice. It is a simple phenomenological model for the high-Tc{T}_{c}Tc​ cuprates that allows both extended (nonlocal) s- and d-wave singlet superconductivity as well as mixed symmetry states. The Hartree-Gor'kov mean-field theory of the model has a finite-temperature phase diagram which shows a transition from pure s-wave to pure d-wave superconductivity, via a mixed symmetry s+ids+ids+id state, as a function of doping. Including Gaussian fluctuations we examine the crossover from weak-coupling BCS superconductivity to the strong-coupling Bose-Einstein condensation of composite s- or d-wave bosons and comment on the origin and symmetry of the pseudogap.
We investigate the zero-temperature BCS to Bose-Einstein crossover at the mean-field level, by driving it with the attractive potential and the particle density. We emphasize specifically the role played by the particle density in this crossover. Three different interparticle potentials are considered for the continuum model in three spatial dimensions, while both s- and d-wave solutions are analyzed for the attractive (extended) Hubbard model on a two-dimensional square lattice. For this model the peculiar behavior of the crossover for the d-wave solution is discussed. In particular, in the strong-coupling limit when approaching half-filling we evidence the occurrence of strong correlations among antiparallel-spin fermions belonging to different composite bosons, which give rise to a quasi-long-range antiferromagnetic order in this limit.