Full counting statistics of spin transfer through the Kondo dot

TL;DR

This paper investigates the full counting statistics of spin transfer in a Kondo quantum dot, analyzing different regimes and limits to understand the distribution of spin and charge transfer, including effects of magnetic fields and asymmetry.

Contribution

It provides a detailed analysis of spin and charge counting statistics in a Kondo dot, comparing exact solutions with generic behavior near the strong-coupling fixed point.

Findings

Spin transfer statistics are trinomial in the Toulouse limit at zero temperature.

Spin-resolved distribution follows a binomial distribution.

Spin and charge measurements become dependent under magnetic field or asymmetry.

Abstract

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.