Full Current Statistics in the Regime of Weak Coulomb Interaction

We evaluate the full statistics of the current via a Coulomb island that is strongly coupled to the leads. This strong coupling weakens Coulomb interaction. We show that in this case the effects of the interaction can be incorporated into the renormalization of transmission eigenvalues of the scatterers that connect the island and the leads. We evaluate the Coulomb blockade gap in the current-voltage characteristics, the value of the gap being exponentially suppressed as compared to the classical charging energy of the island.

Figure 1

Multiterminal ($M=3$) Coulomb island, defined by $M$ multichannel scatterers with transmission coefficients $T_n^{[k]}$.

Figure 2

The energy dependence of the total conductance either saturates (solid lines) or hits zero at Coulomb blockade gap ${\tilde{E}}_C$ (dashed lines). These two scenarios are presented for (a) tunnel connectors, $g_0$ changing from 42 to 14 with the step 4 from upper curve down; (b) diffusive connectors, $g_0$ changing from 18 to 6 with the step 2. Arrows indicate the crossover energy scale $\sim \delta$. We assume $\ln (E_c/\delta )=10.0$.

Figure 3

The probability of big fluctuation of the current $I_3$ at $I_1=I_2$ for the 3-terminal island with identical junctions (Fig. 1). Curves (a)–(d) correspond to diffusive connectors at different values of the renormalization parameter $y(eV)$ [See Eqs. (5)]: (a) 1.0, (b) 0.5, (c)  0.1, (d) 0. No interaction effect is seen for tunnel (1) and ballistic (2) connectors.