The Kondo crossover in shot noise of a single quantum dot with orbital degeneracy

TL;DR

This paper analyzes the shot noise in a multiorbital quantum dot system exhibiting Kondo physics, deriving exact and numerical results for the Fano factor across interaction regimes, revealing a rapid transition from noninteracting to Kondo-dominated behavior.

Contribution

It provides an analytical expression for the Fano factor in multiorbital Kondo systems and combines perturbation theory with numerical renormalization group calculations to explore the crossover behavior.

Findings

Fano factor expressed in terms of Wilson ratio and orbital degeneracy.

Exact calculation of Fano factor for small Coulomb interactions.

Numerical results showing rapid Fano factor transition near the Kondo crossover.

Abstract

We investigate out of equilibrium transport through an orbital Kondo system realized in a single quantum dot, described by the multiorbital impurity Anderson model. Shot noise and current are calculated up to the third order in bias voltage in the particle-hole symmetric case, using the renormalized perturbation theory. The derived expressions are asymptotically exact at low energies. The resulting Fano factor of the backscattering current $F_b$ is expressed in terms of the Wilson ratio $R$ and the orbital degeneracy $N$ as $F_b =\frac{1 + 9(N-1)(R-1)^2}{1 + 5(N-1)(R-1)^2}$ at zero temperature. Then, for small Coulomb repulsions $U$, we calculate the Fano factor exactly up to terms of order $U^5$, and also carry out the numerical renormalization group calculation for intermediate $U$ in the case of two- and four-fold degeneracy ($N=2,\,4$). As $U$ increases, the charge fluctuation in the dot is suppressed, and the Fano factor varies rapidly from the noninteracting value $F_b=1$ to the value in the Kondo limit $F_b=\frac{N+8}{N+4}$, near the crossover region $U\sim \pi \Gamma$, with the energy scale of the hybridization $\Gamma$.