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We investigate the time-dependent transport properties of single and double quantum-impurity systems based on the hierarchical equations of motion (HEOM) approach. In the Kondo regime, the dynamical current in both cases is found oscillating due to the temporal coherence of electrons tunneling through the device, which shares the same mechanism as the single-level resonance without e-e interactions but shows some different characteristics. For single quantum-impurity systems, the temperature T plays an inhibitory action to the oscillations of dynamic current through its suppression to the Kondo effects. The amplitude of the current oscillations is attenuated by the e-e interaction $U$ in the Kondo regime. The frequency of the current oscillation is found almost independent of T and U. For parallel-coupling double quantum-impurity systems, the oscillation of the current shows similar behaviors to the single one, but with two-to-three times larger amplitudes. At the limit of small inter-impurity coupling the oscillation of the current exhibits enhanced characters while it is weakened at the other limit.
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We consider a quantum dot with ${cal K}{geq} 2$ orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multi-level Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel $S{=}1$ Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we derived an effective Hamiltonian at a strong-coupling fixed point. The Hamiltonian capturing the low-energy physics of a two-stage Kondo screening represents the quantum impurity by a two-color local Fermi-liquid. Using non-equilibrium (Keldysh) perturbation theory around the strong-coupling fixed point we analyze the transport properties of the model at finite temperature, Zeeman magnetic field and source-drain voltage applied across the quantum dot. We compute the Fermi-liquid transport constants and discuss different universality classes associated with emergent symmetries.
We investigate thermoelectric transport through a SU(N) quantum impurity in the Kondo regime. The strong coupling fixed point theory is described by the local Fermi-liquid paradigm. Using Keldysh technique we analyse the electric current through the quantum impurity at both finite bias voltage and finite temperature drop across it. The theory of a steady state at zero-current provides a complete description of the Seebeck effect. We find pronounced non-linear effects in temperature drop at low temperatures. We illustrate the significance of the non-linearities for enhancement of thermopower by two examples of SU(4) symmetric regimes characterized by a filling factor m: i) particle-hole symmetric at m=2 and ii) particle-hole non-symmetric at m=1. We analyse the effects of potential scattering and coupling asymmetry on the transport coefficients. We discuss connections between the theory and transport experiments with coupled quantum dots and carbon nanotubes.
Electron transport properties in a parallel double-quantum-dot structure with three-terminals are theoretically studied. By introducing a local Rashba spin-orbit coupling, we find that an incident electron from one terminal can select a specific terminal to depart from the quantum dots according to its spin state. As a result, spin polarization and spin separation can be simultaneously realized in this structure. And spin polarizations in different terminals can be inverted by tuning the structure parameters. The underlying quantum interference that gives rise to such a result is analyzed in the language of Feynman paths for the electron transmission.
Tunneling conductance through two quantum dots, which are connected in series to left and right leads, is calculated by using the numerical renormalization group method. As the hopping between the dots increases from very small value, the following states continuously appear; (i) Kondo singlet state of each dot with its adjacent-site lead, (ii) singlet state between the local spins on the dots, and (iii) double occupancy in the bonding orbital of the two dots. The conductance shows peaks at the transition regions between these states. Especially, the peak at the boundary between (i) and (ii) has the unitarity limit value of $2e^{2}/h$ because of coherent connection through the lead-dot-dot-lead. For the strongly correlated cases, the characteristic energy scale of the coherent peak shows anomalous decrease relating to the quantum critical transition known for the two-impurity Kondo effect. The two dots systems give the new realization of the two-impurity Kondo problem.
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 $1 lesssim N_d lesssim N-1$. It significantly affects the current noise for $N>2$ and the behavior of noise in magnetic fields.
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