Mean-field theory of the Kondo effect in quantum dots with an even number of electrons

We investigate the enhancement of the Kondo effect in quantum dots with an even number of electrons, using a scaling method and a mean field theory. We evaluate the Kondo temperature (formula presented) as a function of the energy difference between spin-singlet and -triplet states in the dot, (formula presented) and the Zeeman splitting, (formula presented) If the Zeeman splitting is small, (formula presented) the competition between the singlet and triplet states enhances the Kondo effect. (formula presented) reaches its maximum around (formula presented) and decreases with (formula presented) obeying a power law. If the Zeeman splitting is strong, (formula presented) the Kondo effect originates from the degeneracy between the singlet state and one of the components of the triplet state at (formula presented) We show that (formula presented) exhibits another power-law dependence on (formula presented) The mean field theory provides a unified picture to illustrate the crossover between these regimes. The enhancement of the Kondo effect can be understood in terms of the overlap between the Kondo resonant states created around the Fermi level. These resonant states provide the unitary limit of the conductance (formula presented)