High-order current correlation functions in the Kondo systems

We examine the statistics of current fluctuations in a junction with a quantum dot described by Kondo Hamiltonian. With the help of modified Keldysh technique we calculate the third current cumulant. As a function of ratio $v=eV∕T_K$ the third cumulant was obtained for three different regimes: Fermi liquid regime $(v<1)$, crossover interval $(v⩾1)$, and RG limit $(v⪢1)$. Unlike the case of noninteracting dot, third momentum shows strong nonlinear voltage dependence. Only in the asymptotical limit $v\to \infty$ the linear dependence on $V$ is recovered.

Figure 1

The four-axis time contour.

Figure 2

The third cumulant $S_3$ versus applied voltage $eV∕T_K$. Dot curve represents MFSB calculations valid for small voltage $eV<T_K$. Solid line with black squares is obtained in NCA approximation. Dash line is the result of direct computation of Eq. (15) with ${\sigma }_0\to \sigma \left(V\right)$. The curves which were calculated for two $T_K$ differing by a factor of 10 practically coincide. This reflects the universality of third cumulant in considered regime. (Inset): Normalized third momentum $\underset{̱}{S}$ as function of $eV∕T$ in the high temperature limit $T⪢T_K$.