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We investigate the charge fluctuations of a single-electron box (metallicgrain) coupled to a lead via a smaller quantum dot in the Kondo regime. Themost interesting aspect of this problem resides in the interplay between spinKondo physics stemming from the screening of the spin of the small dot andorbital Kondo physics emerging when charging states of the grain with (charge)Q=0 and Q=e are almost degenerate. Combining Wilson's numericalrenormalization-group method with perturbative scaling approaches we pushforward our previous work [K. Le Hur and P. Simon, Phys. Rev. B 67, 201308R(2003)]. We emphasize that for symmetric and slightly asymmetric barriers, thestrong entanglement of charge and spin flip events in this setup inevitablyresults in a non trivial stable SU(4) Kondo fixed point near the degeneracypoints 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 Coulombstaircase behavior and hampers the Matveev logarithmic singularity to arise.Most notably, the associated Kondo temperature $T_K^{SU(4)}$ might be raisedcompared to that in the conductance experiments through a small quantum dot$(\sim 1K)$ which makes the observation of our predictions a priori accessible.We discuss the robustness of the SU(4) correlated state against the inclusionof an external magnetic field, a deviation from the degeneracy points,particle-hole symmetry in the small dot, asymmetric tunnel junctions andcomment on the different crossovers.Comment: 17 pages, 2 columns, 13 figures (extend cond-mat/0210342

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