Full Counting Statistics for Orbital-Degenerate Impurity Anderson Model with Hund’s Rule Exchange Coupling

Abstract

We study nonequilibrium current fluctuations through a quantum dot, which includes a ferromagnetic Hund's rule coupling J, in the low-energy Fermi liquid regime using the renormalized perturbation theory. The resulting cumulant for the current distribution in the particle-hole symmetric case shows that spin-triplet and spin-singlet pairs of quasiparticles are formed in the current due to the Hund's rule coupling, and these pairs enhance the current fluctuations. In the fully screened higher-spin Kondo limit, the Fano factor takes a value F(b)=(9M+6)/(5M+4) determined by the orbital degeneracy M. We also investigate the crossover between the small and large J limits in the two-orbital case M=2, using the numerical renormalization group approach.

Transport properties of the Coulomb–Majorana junction

“…(Intra-lead interactions, g < 1, weakly affect this result [53].) When additional orbital degeneracies are present, an SU (N ) variant of this scenario can be realized, where local Fermi liquid theory holds again [54][55][56][57]. The Fano factor remains universal (but different from 5/3) in the SU (N ) Kondo regime, cf [55, table 1].…”

Current cross-correlation in the Anderson impurity model with exchange interaction

“…This form of the shot noise has already been derived for Hund's rule exchange interaction J < 0, 16 and here it is naturally extended to the whole of the local-Fermi-liquid region, including antiferromagnetic interaction J > 0. The Fano factor for the backscattering current is given by the ratio of the shot noise and the nonlinear current as…”

“…The low-energy state for the ferromagnetic exchange interaction is simply described by the S = N/2 Kondo state for any orbital degeneracy N and the extension can be readily obtained. 16 However, discussion on the ground state for the antiferromagnetic exchange interaction contains more variety. For instance, the model for even N has a critical interaction J c and the conduction electrons decouple from the dot for J > J c , similarly to the case of N = 2 discussed in the last section.…”

“…The counter terms cancel all the terms with higher orders in the renormalized interactions. 16,21,22,34 We shall calculate current crosscorrelation by the perturbation expansion in the renormalized interactions.…”

“…By classifying the backscattered current by the effective charges, 16 the ratio of probability to generate current with effective charge e and 2e are found to be 4:7, which result in the value through Eq. (78).…”