Two-channel versus infinite-channel Kondo models for the single-electron transistor

We investigate the low-temperature dynamics of single electron boxes and tr ansistors close to their degeneracy point using renormalization-group metho ds. We show that intermode scattering is a relevant perturbation and always drives the system to the two-channel Kondo fixed point, where the two chan nels correspond to the real spins of the conduction electrons. However, the crossover temperature T*, below which Matveev's two-channel Kondo scenario [K.A. Matveev, Phys. Rev. B 51, 1743 (1995)] develops decreases exponentia lly with the number of conduction modes in the tunneling junctions and is e xtremely small in most cases. Above T* the "infinite channel model" of G. F alci, G. Schon, and G.T. Zimany, Phys. Rev. Lett. 74, 3257 (1995) turns out to be a rather good approximation. We discuss the experimental limitations and suggest an experimental setup to observe the multichannel Kondo behavi or.