Nondivergent calculation of unwanted high-order tunneling rates in single-electron devices

Recently developed single-electron devices are based on the control of electron tunneling across each tunnel junction of the circuit. However, unwanted higher-order tunneling processes, referred to as cotunneling processes, modify this simple picture and reduce the accuracy of the devices. We calculate the cotunneling rate in a linear array of tunnel junctions beyond the lowest order of perturbation theory by partially resumming the infinite perturbation expansion for the energy of a metastable state. We apply this calculation to the transition between two different tunneling regimes in various single-electron circuits.