The 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 \(F_b =\frac{1 + 9(N-1)(R-1)^2}{1 + 5(N-1)(R-1)^2}\) 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 \(\Gamma\).