Cotunneling and renormalization effects for the single-electron transistor

We study electron transport through a small metallic island in the perturbative regime. Using a diagrammatic real-time technique, we calculate the occupation of the island as well as the conductance through the transistor at arbitrary temperature and bias voltage in forth order in the tunneling matrix elements, a process referred to as cotunneling. Our formulation does not require the introduction of a cutoff. At resonance we find significant modifications of previous theories and quantitative agreement with recent experiments. We determine the renormalization of the system parameters and extract the arguments of the leading logarithmic terms (which can not be derived from usual renormalization group analysis). Furthermore, we perform the low- and high-temperature limits. In the former, we find a behavior characteristic for the multichannel Kondo model.