Spin Fractionalization of an Even Number of Electrons in a Quantum Dot

We find that Kondo resonant conductance can occur in a quantum dot in the Coulomb blockade regime with an even number of electrons $N$. The contacts are attached to the dot in a pillar configuration, and a magnetic field $B_{\perp }$ along the axis is applied. $B_{\perp }$ lifts the spin degeneracy of the dot energies. Usually, this prevents the system from developing the Kondo effect. Tuning $B_{\perp }$ to the value $B^{*}$ where levels with different total spin cross restores both the degeneracy and the Kondo effect. We analyze a dot charged with $N=2\mathrm{}$ electrons. Coupling to the contacts is antiferromagnetic due to a spin selection rule and, in the Kondo state, the charge is unchanged while the total spin on the dot is $S=1\mathrm{}/2$.