Superconductivity in theSU(N)Anderson lattice atU=∞

Abstract

We present a mean-field study of superconductivity in a generalized N -channel cubic Anderson lattice at U = ∞ taking into account the effect of a nearest-neighbor attraction J. The condition U = ∞ is implemented within the slave-boson formalism considering the slave bosons to be condensed. We consider the f -level occupancy ranging from the mixed valence regime to the Kondo limit and study the dependence of the critical temperature on the various model parameters for each of three possible Cooper pairing symmetries (extended s, d-wave and p-wave pairing) and find interesting crossovers. It is found that the d− and p− wave order parameters have, in general, very similar critical temperatures. The extended s-wave pairing seems to be relatively more stable for electronic densities per channel close to one and for large values of the superconducting interaction J.

Heavy-fermion superconductivity: AnX-boson treatment

“…This behavior is in agreement to experimental results, since superconductivity was found both in heavy fermion materials as well as in intermediate valence compounds [37,38]. Moreover, we show that higher values of the hybridization parameter implies in lower values associated to the maximum of the superconducting critical temperature, indicating that the real charge exchange between bands tends to destabilizes the Cooper pairing, in agreement to the previous results obtained by the slave-boson approach [3] and by perturbative approach [2]. Furthermore, as the total occupation is raised and for larger V , the system presents a superconductor-insulator transition, which is related to the appearance of a hybridization gap that cannot be obtained by the slave-boson method, which breaks down in this region.…”

“…In the large N t regime the f level is almost fully occupied with one electron per state and the ρ f (µ) decreases causing the suppression of superconductivity, but it should be noted that T c vanishes before N f → 1. Similar results were also obtained by Araújo et al [3], except that for them the superconducting critical temperature is constrained to T c ≤ T K , where the Kondo temperature T K is defined as the T that makes the slave-boson parameter z vanish. Indeed, in the slave-boson method by increasing the temperature T or the chemical potential µ the valuẽ V ≡ √ zV = 0 is presently reached, leading to N f → 1 and the decouple of the two types of electrons, what can be interpreted as a change of phase related to a symmetry breaking of the mean-field Hamiltonian.…”

“…al. [3]. Further, in the absence of the hybridization term the f -band and the conduction band decouples and solving the remaining system of equations for the f -band one formally recover the BCS result though with a distinct physical meaning, here the energy E f assumes a constant value and the strong correlations presented are taken into consideration via the parameter D σ .…”

“…al. [3]. Moreover, Tachiki and Maekawa [29] studied the superconductivity in the Periodic Anderson Model with a small dispersion of the f -band in the heavy fermion state and they have concluded that pairing between f -electrons are responsible for superconductivity, rather than between the conduction electrons.…”

Magnetic impurities in a superconductor: Effect of domain walls and interference

“…However, in the Ce-based heavy-fermions magnetism typically competes with superconductivity. It has been found in the context of the Anderson model that, both in the problem of local moment formation in the superconductor 39 and in the context of the Anderson lattice model, that, in a certain regime, a quantum phase transition is found 40 which is characterized by an abrupt expulsion of magnetic order by d-wave superconductivity, as an externally applied pressure increases. This transition takes place when the d-wave superconducting critical temperature, T c , intercepts the magnetic critical temperature, T m , under increasing pressure.…”