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, $n_c$, 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.

12 pages, 12 figures

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• Superconducting Kondo phase in an orbitally-separated bilayer
• Interplay between charge, magnetic and superconducting order in a Kondo lattice with an attractive Hubbard interaction
• Reentrant $s$-wave superconductivity in the periodic Anderson model with attractive conduction band Hubbard interaction