Current characteristics of the single-electron transistor at the degeneracy point

The linear and nonlinear transport properties of the single-electron transistor at the degeneracy point are investigated for the case of weak single-mode tunnel junctions. Two opposing scenarios are considered, distinguished by whether or not electrons can propagate coherently between the two tunnel junctions. Each of these two scenarios corresponds to the realization of a different multichannel Kondo effect - the two-channel Kondo effect in the case where coherent propagation is allowed, and the four-channel Kondo effect in the absence of coherent propagation. A detailed analysis of the linear and nonlinear conductance is presented for each of these scenarios, within a generalized noncrossing approximation for the nonequilibrium multichannel Kondo Hamiltonian. A zero-bias anomaly is shown to develop with decreasing temperature, characterized by the anomalous power laws of the multichannel Kondo effect. A scaling function of the differential conductance with V/T (V being the applied voltage bias, T the temperature) is proposed as a distinctive experimental signature for each of these two scenarios. In the absence of coherent propagation between the leads, and for asymmetric couplings to the two leads, a crossover from four-channel to two-channel behavior is manifested in a vanishing zero-temperature conductance, and in a nonmonotonic voltage dependence of the differential conductance for small asymmetries.