We study Bell-state correlations for quasiparticle pairs excited in nonlinear current through a double quantum dot in the Kondo regime. Exploiting the renormalized perturbation expansion in the residual interactions of the local Fermi liquid and Bell's inequality for cross correlation of spin currents through distinct conduction channels, we derive an asymptotically exact form of Bell's correlation for the double dot at low bias voltages. We find that pairs of quasiparticles and holes excited by the residual exchange interaction violate Bell's inequality for the spin currents.
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.
We study how bias and tunneling asymmetries affect nonlinear current through a quantum dot with
N discrete levels in the Fermi liquid regime, using an exact low-energy expansion of the current derived up to terms of order
V3 with respect to the bias voltage. The expansion coefficients are described in terms of the phase shift, the linear susceptibilities, and the three-body correlation functions, defined with respect to the equilibrium ground state of the Anderson impurity model. In particular, the three-body correlations play an essential role in the order
V3 term, and their coupling to the nonlinear current depends crucially on the bias and tunnel asymmetries. The number of independent components of the three-body correlation functions increases with
N the internal degrees of the quantum dots, and it gives a variety in the low-energy transport. We calculate the correlation functions over a wide range of electron fillings of the Anderson impurity model with the
SU(N) internal symmetry, using the numerical renormalization group. We find that the order
V3 nonlinear current through the
SU(N) Kondo state, which occurs at electron fillings of 1 and $N\ensuremath{-}1$ for strong Coulomb interactions, significantly varies with the three-body contributions as tunnel asymmetries increase. Furthermore, in the valence fluctuation regime toward the empty or fully occupied impurity state, a sharp peak emerges in the coefficient of
V3 current in the case at which bias and tunneling asymmetries cooperatively enhance the charge transfer from one of the electrodes.
We analyze the full counting statistics of the multiorbital Kondo effect in a quantum dot with SU(
N) symmetry in the framework of renormalized perturbation theory. The current probability distribution function is calculated for an arbitrary dot-site Coulomb repulsion
U 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
e and
2e, with different
N dependences. The cross correlation between different orbital currents shows exponential enhancement with respect to
U, which directly addresses the formation of the orbital-singlet state.
We present a microscopic Fermi liquid view on the low-energy transport through an Anderson impurity with N discrete levels, at arbitrary electron filling N_{d}. It is applied to nonequilibrium current fluctuations, for which the two-quasiparticle collision integral and the three-body correlations that determine the quasiparticle energy shift play important roles. Using the numerical renormalization group up to N=6, we find that for strong interactions the three-body fluctuations are determined by a single parameter other than the Kondo energy scale in a wide filling range 1≲N_{d}≲N-1. It significantly affects the current noise for N>2 and the behavior of noise in magnetic fields.
We apply a combination of numerical renormalization group (NRG) and renormalized perturbation theory (RPT) to a model of two quantum dots (impurities) described by two Anderson impurity models hybridized to their respective baths. The dots are coupled via a direct Coulomb interaction
U12 and a spin exchange interaction
J. The model has two types of quantum critical points, one at
J=Jc to a local singlet state and one at
U12=U12c to a locally charge ordered state. The renormalized parameters which determine the low energy behavior are calculated from the NRG. The results confirm the values predicted from the RPT on the approach to the critical points, which can be expressed in terms of a single energy scale
T∗ in all cases. This includes cases without particle-hole symmetry, and cases with asymmetry between the dots, where there is also a transition at
J=Jc. The results give a comprehensive quantitative picture of the behavior of the model in the low energy Fermi liquid regimes, and some of the conclusions regarding the emergence of a single energy scale may apply to a more general class of quantum critical points, such as those observed in some heavy fermion systems.