Perturbation theory for the two-impurity Kondo problem-RKKY-induced vanishing of the Kondo temperature

Abstract

The authors consider the two-impurity Kondo problem, in a basis in which the electron states are written in terms of their parity, with respect to the midpoint between impurities. They consider the scattering of electrons by the spin-one complexes formed by the impurities, making use of the fact that the RKKY interaction is diagonal in this basis and acts in much the same way that a crystal field acts in the degenerate Kondo problem. By expanding the equations of motion to leading logarithmic order the authors show that the resulting Kondo temperature is reduced by an increasing antiferromagnetic RKKY interaction, and for one of the electron parity channels crosses the antiferromagnetic RKKY singles. This happens when the RKKY interaction is of the order of the bare (no RKKY) Kondo temperature. The authors interpret this crossing as reflecting the divergence of Fermi liquid properties found in numerical studies along the lines of a phenomenological model introduced by two of the authors.