Stochastic Coulomb blockade in a double-dot system

Abstract

Coulomb blockade in a system of two dots connected in series is qualitatively different from that of a single dot. We show that, although the conductance G of a double-dot system reveals oscillations with the gate-induced potential ${\mathit{V}}_{\mathit{g}}$, a typical period of these oscillations changes with the temperature. If the capacitance ratio ${\mathit{C}}_1$/${\mathit{C}}_2$ for the dots is an irrational number, the system of peaks in G(${\mathit{V}}_{\mathit{g}}$) becomes increasingly sparse as the temperature decreases. Both the peak-to-peak distance and the activation energies of the conductance at the peaks that persist are random. However, the distribution function of activation energies calculated for a large interval of ${\mathit{V}}_{\mathit{g}}$ has a universal shape and may be considered as a characteristic pattern of a double-dot system. If the ratio ${\mathit{C}}_1$/${\mathit{C}}_2$ is small, there is a substantial range of intermediate temperatures in which the ordinary periodic Coulomb oscillations are restored. Numerical simulations show that for observation of both stochastic and regular Coulomb blockade for the same sample at different temperatures it is enough to have the ratio ${\mathit{C}}_1$/${\mathit{C}}_2$≤0.5. The existence of a small interdot capacitance C≪${\mathit{C}}_1$,${\mathit{C}}_2$ is shown to cause, at the lowest temperatures, a splitting of the conductance peaks that persist into doublets with a constant spacing ${\mathit{e}}^2$C/${\mathit{C}}_1$ ${\mathit{C}}_2$.