Strong tunneling in double-island structures

We study the electron transport through a system of two low-capacitance metal islands connected in series between two electrodes. The work is motivated in part by experiments on semiconducting double dots, which show intriguing effects arising from coherent tunneling of electrons and mixing of the single-electron states across tunneling barriers. In this article, we show how coherent tunneling affects metallic systems and leads to a mixing of the macroscopic charge states across the barriers. We apply a recently formulated renormalization-group (RG) approach to examine the linear response of the system with high tunnel conductances (up to ${8e}^2/h).\mathrm{}$ In addition we calculate the (second order) cotunneling contributions to the nonlinear conductance. Our main results are that the peaks in the linear and nonlinear conductance as a function of the gate voltage are reduced and broadened in an asymmetric way, as well as shifted in their positions. In the limit where the two islands are coupled weakly to the electrodes, we compare to theoretical results obtained by Golden and Halperin and Matveev et al. In the opposite case when the two islands are coupled more strongly to the leads than to each other, the peaks are found to shift, in qualitative agreement with the recent prediction of Andrei et al. for a similar double-dot system, which exhibits a phase transition.