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

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 ${F}_{b}=\frac{1+9(N\ensuremath{-}1)(R\ensuremath{-}1){}^{2}}{1+5(N\ensuremath{-}1)(R\ensuremath{-}1){}^{2}}$ 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 twofold and fourfold 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 $U~\ensuremath{\pi}\ensuremath{\Gamma}$, with the energy scale of the hybridization $\ensuremath{\Gamma}$.