Two-state approximation in the Coulomb-blockade theory: Simple analytical results for a double-tunnel junction

Abstract

Under the conditions of a Coulomb blockade in a strongly asymmetric mesoscopic double-junction system it is valid to consider only two possible charge states in the interjunction region. Within this two-state approximation, a simple analytical form for the dependence of differential conductance G on voltage V is found. The oscillatory part of G(V) is proportional to (1/γn){(ν/γn)+1${\mathrm{\}}}^{\mathrm{-}2}$, where ν=(V-${\mathit{V}}_{\mathit{n}}$)/ΔV, ${\mathit{V}}_{\mathit{n}}$ is the threshold voltage for the nth step in the I-V characteristic, and ΔV=e/${\mathit{C}}_2$ is the period. The validity of the approximation is checked by a comparison with the numerical solution of the rate equations for the double junction. These analytical results permit the estimation of junction parameters from the slopes measured at the critical points of an I-V curve exhibiting a Coulomb staircase.