Variation of the Coulomb staircase in a two-junction system by fractional electron charge

We report a measurement of the Coulomb staircase in a two-junction system where the fractional residual charge Q₀ on the center electrode is varied without an external electrode. We present a simple analytic equation for I (V) that depends on the parameters of the junctions, C₁, ₂, R₁, ₂, and Q₀, and allows us to obtain them directly from the data. Full ``orthodox'' theory simulations incorporating these parameters are in remarkable agreement with our data. Asymmetric gaplike features in the I-V curve are seen to vary with Q₀, and can be well understood by use of a C₂/C₁-Q₀ phase diagram.