Full counting statistics of spin transfer through a Kondo dot

We calculate the spin current distribution function for a Kondo dot in two different regimes. In the exactly solvable Toulouse limit, the linear response, zero-temperature statistics of the spin transfer is trinomial, such that all the odd moments vanish and the even moments follow a binomial distribution. On the contrary, the corresponding spin-resolved distribution turns out to be binomial. The combined spin and charge statistics is also determined. In particular, we find that, in the case of a finite magnetic field or an asymmetric junction, the spin and charge measurements become statistically dependent. Furthermore, we analyzed the spin counting statistics of a generic Kondo dot at and around the strong-coupling fixed point (the unitary limit). Comparing these results with the Toulouse limit calculation, we determine which features of the latter are generic and which ones are artifacts of the spin symmetry breaking.

Figure 1

Schematic representation of the process $T_2$.

Figure 2

Current-noise ratio in units of $V∕{\Gamma }_{+}$ for the spin current as a function of applied magnetic field.

Figure 3

Normalized spin-charge current correlation in units of $V∕{\Gamma }_{+}$ as a function of magnetic field for different values of ${\Gamma }_{-}$.