Calculation of the Nondivergent Cotunneling Rates in a Double Tunnel Junction Embedded in a Dissipative Electromagnetic Environment

We consider two serially connected tunnel junctions embedded in a dissipative electromagnetic environment. Within the Coulomb blockade region where the sequential single electron tunneling is suppressed, electron transport through the whole system is achieved via higher-order tunneling processes. The standard approach using perturbation theory to fourth order in the tunnel Hamiltonian gives divergent rates of these processes at the Coulomb blockade boundary. By using a diagrammatic technique, we perform an analytic summation over a perturbative expansion of infinite order. In this way, we remove the divergence and derive an expression for the cotunneling current applicable over the whole Coulomb blockade region.