Simple Self-Consistent Treatment of Kondo's Effect in Dilute Alloys

Abstract

Thye self-consistent treatment of Kondo's effect by Nagaoka is revised by using the method of Gor'kov in the theory of superconductivity. Expressing the spin operators in terms of Fermi operators, such as sz = (a↑+a↑-a↓+a↓)/2, the Green's functions of the type ≪≪ck′↑Sz|ck ↑>> are decomposed into the sum of terms like ≪a↑+ck′↑>≪≪a↑|ck ↑+>>. The existence of these terms implies the existence of the bound state between the localized spin and the spin density of conduction electrons. Essentially the same expression for the Green's function of conduction electrons as in Nagaoka's treatment is obtained, but we also have the bound state in the case of ferromagnetic coupling.