Maximized orbital and spin Kondo effects in a single-electron transistor

We investigate the charge fluctuations of a single-electron box (metallic grain) coupled to a lead via a smaller quantum dot in the Kondo regime. The most interesting aspect of this problem resides in the interplay between spin Kondo physics stemming from the screening of the spin of the small dot and orbital Kondo physics emerging when charging states of the grain with (charge) Q=0 and Q=e are almost degenerate. Combining Wilson's numerical renormalization-group method with perturbative scaling approaches we push forward our previous work [K. Le Hur and P. Simon, Phys. Rev. B 67, 201308R (2003)]. We emphasize that, for symmetric and slightly asymmetric barriers, the strong entanglement of charge and spin flip events in this setup inevitably results in a nontrivial stable SU(4) Kondo fixed point near the degeneracy points of the grain. By analogy with a small dot sandwiched between two leads, the ground state is Fermi-liquid-like, which considerably smears out the Coulomb staircase behavior and prevents the Matveev logarithmic singularity from arising. Most notably, the associated Kondo temperature T-K(SU(4)) might be raised compared to that in conductance experiments through a small quantum dot (similar to1 K), which makes the observation of our predictions a priori accessible. We discuss the robustness of the SU(4) correlated state against the inclusion of an external magnetic field, a deviation from the degeneracy points, particle-hole symmetry in the small dot, and asymmetric tunnel junctions and comment on the different crossovers.