Coulomb blockade and current-voltage characteristics of ultrasmall double tunnel junctions with external circuits

Abstract

The theory on the Coulomb blockade in ultrasmall double junctions with external circuits is proposed, which self-consistently describes tunneling currents and charged states of islands without resorting to the stochastic technique. The island Hamiltonian in the theory contains the chemical potential (charged state) of the island to be determined self-consistently through the current continuity conditions. A general expression for the tunneling current is obtained together with self-consistency equations for the charge state of the island. Current-voltage characteristics are discussed analytically at zero temperature in the limits of high and low impedance environments. Coulomb gaps and the difference in current-voltage characteristics between symmetric and asymmetric double junctions (Coulomb staircases) were also analytically discussed in connection with the concept of neutral and charged islands. At finite temperatures current-voltage characteristics and the number of charges on the island under equilibrium configuration is calculated numerically for various junction parameters and temperatures. The theory describes reasonably well the fundamental features of the ultrasmall double junctions with external circuits.