Suppression of the Kondo effect in quantum dots by even-odd asymmetry

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 (${\mathit{J}}_{\mathit{d}}$) that is inherently present among the electrons occupying the various quantum levels of the dot. We show explicitly that for ferromagnetic coupling (${\mathit{J}}_{\mathit{d}}$≳0), an s-d exchange for an S=1 Kondo problem is recovered. In contrast, for the antiferromagnetic case, ${\mathit{J}}_{\mathit{d}}$<0, we find that the Kondo effect is present only if there are an odd number of electrons on the dot. In addition, we find that spin exchange produces a second period as well as additional fine structure in the conductance that is consistent with experimental measurements.