Full counting statistics for the Kondo dot

TL;DR

This paper calculates the full counting statistics of charge transport in Kondo and Luttinger liquid models, revealing electron and pair tunneling contributions and providing explicit cumulant formulas.

Contribution

It introduces a unified approach to compute charge cumulants in Kondo and Luttinger models, including explicit third cumulant calculations and simplified formulas at specific interaction parameters.

Findings

Transport involves electron and pair tunneling.

Explicit third cumulant ('skewness') derived.

Statistics simplify at g=1/2, resembling a modified Levitov–Lesovik formula.

Abstract

The generating function for the cumulants of charge current distribution is calculated for two generalised Majorana resonant level models: the Kondo dot at the Toulouse point and the resonant level embedded in a Luttinger liquid with the interaction parameter $g=1/2$. We find that the low--temperature non-equilibrium transport in the Kondo case occurs via tunnelling of physical electrons as well as by coherent transmission of electron pairs. We calculate the third cumulant (`skewness') explicitly and analyse it for different couplings, temperatures, and magnetic fields. For the $g=1/2$ set-up the statistics simplifies and is given by a modified version of the Levitov--Lesovik formula.