We analyze here a model for single-electron charging in semiconductor quantum dots that includes the standard Anderson on-site repulsion (U) as well as the spin-exchange (Jd) that is inherently present among the electrons occupying the various quantum levels of the dot. A Schrieffer-Wolff-type transformation is developed to analyze this model. We show explicitly that for ferromagnetic coupling (Jd > 0), an s-d exchange for an S = 1 Kondo problem is recovered. In contrast, for the antiferromagnetic case, Jd > 0, we find that the Kondo effect is present only if there are an odd number of electrons on the dot. Spin-exchange is then shown to produce a second period in the conductance that is consistent with experimental measurements.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics