A mean-field approach to Kondo-attractive-Hubbard model

Abstract

With the purpose of investigating coexistence between magnetic order and superconductivity, we consider a model in which conduction electrons interact with each other, via an attractive Hubbard on-site coupling U, and with local moments on every site, via a Kondo-like coupling, J. The model is solved on a simple cubic lattice through a Hartree-Fock approximation, within a 'semi-classical' framework which allows spiral magnetic modes to be stabilized. For a fixed electronic density, n , the small J region of the ground state (T = 0) phase diagram displays spiral antiferromagnetic (SAFM) states for small U. Upon increasing U, a state with coexistence between superconductivity (SC) and SAFM sets in; further increase in U turns the spiral mode into a Néel antiferromagnet. The large J region is a (singlet) Kondo phase. At finite temperatures, and in the region of coexistence, thermal fluctuations suppress the different ordered phases in succession: the SAFM phase at lower temperatures and SC at higher temperatures; also, reentrant behaviour is found to be induced by temperature. Our results provide a qualitative description of the competition between local moment magnetism and superconductivity in the borocarbides family.

Reentrant s-wave superconductivity in the periodic Anderson model with attractive conduction band Hubbard interaction

“…This generically leads to d-wave pairing, though recent studies on CeCu 2 Si 2 surprisingly indicated a fully gapped s-wave state 20 . Hence, theoretical work on the systems with periodic magnetic moments was mostly focused on unconventional d-wave pairing near the antiferromagnetic quantum critical point in the Kondo/Anderson lattice model [21][22][23] , with few exceptions that treated attractive on-site pairing interaction in the Kondo lattice model [24][25][26][27] .…”

Superconducting Kondo phase in an orbitally separated bilayer

“…Therefore, as we tune in U , J, t z (<4t), and the band filling competing effects may emerge between superconducting (SC), antiferromagnectic (AFM), and singlet (Kondo) phases. In order to investigate the main features of this competition, we adopt a Hartree-Fock approach [24] which allows us to probe the occurrence of spiral magnetic phases characteristic of the KLM [19]. To this end, we write the spin operators for the d and f orbitals in a fermionic basis as…”

“…where T is the time ordering operator, τ is the time, and α = c, d, and f . Taking the time Fourier transform and 1 We have checked the contribution of triplet hybridization terms [19,24], and found that they are negligible. performing an analytical continuation allow one to obtain the spectral function,…”

“…The quest for alternative scenarios leading to superconductivity in KLM-like models is therefore a question of current interest. In particular, we note that the Kondo singlet phase (both the insulator at half filling and the doped metallic phase) seems to be quite robust, since the inclusion of local pairing interactions between the conduction electrons only stabilizes superconductivity in the strong attractive coupling limit, or in the weak d-f exchange coupling [24,25]. One possible route towards superconductivity is the introduction of an extra layer, with the purpose of altering the band structure in a fundamental way.…”

“…As a first step towards a better understanding of the nature of such an interface, it is convenient to resort to less restrictive methodologies. Thus we use an unrestricted Hartree-Fock approximation [19,24] to investigate the properties of this system. Despite working on a two-dimensional lattice, our results should serve as a qualitative guide both to the interplay between opposing tendencies in the ground state, and to a three-dimensional construction, with the two layers as the repeating unit.…”