Kondo ground state in a quantum dot with an even number of electrons in a magnetic field

Kondo conduction has been observed in a quantum dot with an even number of electrons at the triplet-singlet degeneracy point produced by applying a small magnetic field B orthogonal to the dot plane. At a much larger field $B\sim B_{*},$ orbital effects induce the reversed transition from the singlet to the triplet state. We study the newly proposed Kondo behavior at this point. Here the Zeeman spin splitting cannot be neglected, which changes the nature of the Kondo coupling. On the grounds of exact diagonalization results in a dot with cylindrical symmetry, we show that, at odds with what happens at the other crossing point, close to $B_{*},$ orbital and spin degrees of freedom are “locked together,” so that the Kondo coupling involves a fictitious spin $\frac{1}{2}$ only, which is fully compensated for by conduction electrons under suitable conditions. In this sense, spin at the dot is fractionalized. We derive the scaling equation of the system by means of a nonperturbative variational approach. The approach is extended to the $B\ne B_{*}$ case and the residual magnetization on the dot is discussed.