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 (Jd) that is inherently present among the electrons occupying the various quantum levels of the dot. 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. In addition, we find that spin-exchange produces a second period in the conductance that is consistent with experimental measurements. PACS numbers: Typeset using REVTEX 1 When a gate voltage is applied to a nano-scale semiconductor inversion layer (or quantum dot), electrons will flow one at a time across this device provided that the applied voltage is an integral multiple of the capacitance charging energy of the quantum dot. Experiments illustrating the principle of charge quantization by virtue of the charging energy have been performed recently on numerous semiconductor [1] [2] [3] [4] [5] as well as superconducting [6] nano-structures. We focus here solely on the semiconductor devices. It is now well-accepted [5] that in semiconductor quantum dots, the dominant contribution to the capacitance charging energy, Ec = e 2C arises from the on-site Coulomb repulsion. Here C is the capacitance between the quantum dot, the tunnel junctions, and the electrical leads connected to the dot. Transport in quantum dots will be Coulomb limited if kBT < EC and kBT > ∆ǫ, where ∆ǫ is the spacing between the single particle states of the dot. Because of the central role played by on-site Coulomb repulsions in the transport properties of quantum dots, it is natural to model a quantum dot with a Hubbard-like model. In so far as a quantum dot can be reduced to a single site [7] with a charging energy U, the Anderson model [8] for the interaction of a magnetic defect coupled to a non-interacting sea of conduction electrons is appropriate [7]: HA = ∑