Cotunneling and renormalization effects for the single-electron transistor

We consider transport properties through a small metallic island in the perturbative regime. For this purpose we present a diagrammatic expansion of the reduced density matrix up to fourth order in the tunneling matrix elements (cotunneling). Improving our previous theory, we are able to calculate the occupation of the island as well as the conductance through the transistor at arbitrary temperature and bias voltage. Furthermore, we determine the renormalization of the system parameters and extract the arguments of the leading logarithmic terms (which cannot be derived from usual renormalization-group analysis). We perform the low- and high-temperature limits. In the former, we find a behavior characteristic for the multichannel Kondo model. We find quantitative agreement with recent experiments.