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arXiv:1201.1957 · Physical Review Letters

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

Rui Sakano, Yunori Nishikawa, Akira Oguri, Alex C. Hewson, Seigo Tarucha

Published Jun 26, 2012• 15 citations
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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.

DOI
10.1103/physrevlett.108.266401

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We analyze the full counting statistics of the multiorbital Kondo effect in a quantum dot with SU(NNN) symmetry in the framework of renormalized perturbation theory. The current probability distribution function is calculated for an arbitrary dot-site Coulomb repulsion UUU in the particle-hole-symmetric case. The resulting cumulant up to the leading nonlinear term of applied bias voltages indicates two types of electron transfer, respectively carrying charge eee and 2e2e2e, with different NNN dependences. The cross correlation between different orbital currents shows exponential enhancement with respect to UUU, which directly addresses the formation of the orbital-singlet state.
Studies of the effects of the Hund's rule coupling JH{J}_{H}JH​ in multiple orbit impurities or quantum dots using different models have led to quite different predictions for the Kondo temperature TK{T}_{K}TK​ as a function of JH{J}_{H}JH​. We show that the differences depend on whether or not the models conserve orbital angular momentum about the impurity site. Using numerical renormalization-group calculations, we deduce the renormalized parameters for the Fermi liquid regime and show that, despite the differences between the models, the low-energy fixed point in the strong-correlation regime is universal, with a single energy scale TK{T}_{K}TK​ and just two renormalized interaction parameters, a renormalized single orbital term, $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{U}=4{T}_{K}$, and a renormalized Hund's rule term, ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}}_{H}=8{T}_{K}/3$.
We study spin entanglement of the quasiparticles of the local Fermi liquid excited in nonlinear current through a quantum dot described by the Anderson impurity model with two degenerate orbitals coupled to each other via an exchange interaction. Applying the renormalized perturbation theory, we obtain the precise form of the cumulant generating function and cross-correlations for the currents with spin angled to arbitrary directions, up to third order in the applied bias voltage. It is found that the exchange interaction gives rise to spin-angle dependency in the cross-correlation between the currents through the two different orbitals and also brings an intrinsic cross-correlation of currents with three different angular momenta.
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