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arXiv:1410.1235 · New Journal of Physics

Time-dependent transport through quantum-impurity systems with Kondo resonance

YongXi Cheng, WenJie Hou, YuanDong Wang, ZhenHua Li, JianHua Wei, YiJing Yan

Published Mar 3, 2015• 37 citations
arXivHTMLPDF

Abstract

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 oscillates with time in both cases 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 has an inhibitory effect on the oscillations of dynamic current through its suppression of 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 oscillations is found almost independent of T and U . For parallel-coupling double quantum-impurity systems, the oscillation of the current shows similar behavior 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.

DOI
10.1088/1367-2630/17/3/033009

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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 oscillates with time in both cases 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 has an inhibitory effect on the oscillations of dynamic current through its suppression of 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 oscillations is found almost independent of T and U . For parallel-coupling double quantum-impurity systems, the oscillation of the current shows similar behavior 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.
A systematic study is performed on time-dependent dynamic transport characteristics of a side-coupled double-quantum-impurity system based on the hierarchical equations of motion. It is found that the transport current behaves like a single quantum dot when the coupling strength is low during tunneling or Coulomb coupling. For the case of only tunneling transition, the dynamic current oscillates due to the temporal coherence of the electron tunneling device. The oscillation frequency of the transport current is related to the step voltage applied by the lead, while temperature T, electron–electron interaction U and the bandwidth W have little influence. The amplitude of the current oscillation exists in positive correlation with W and negative correlation with U. With the increase in coupling t 12 between impurities, the ground state of the system changes from a Kondo singlet of one impurity to a spin singlet of two impurities. Moreover, lowering the temperature could promote the Kondo effect to intensify the oscillation of the dynamic current. When only the Coulomb transition is coupled, it is found that the two split-off Hubbard peaks move upward and have different interference effects on the Kondo peak at the Fermi surface with the increase in U 12, from the dynamics point of view.
We study the real-time dynamics of the Kondo effect after a quantum quench in which a magnetic impurity is coupled to two metallic Hubbard chains. Using an effective field theory approach, we find that for noninteracting electrons the charge current across the impurity is given by a scaling function that involves the Kondo time. In the interacting case, we show that the Kondo time decreases with the strength of the repulsive interaction and the time dependence of the current reveals signatures of the Kondo effect in a Luttinger liquid. In addition, we verify that the relaxation of the impurity magnetization does not exhibit universal scaling behavior in the perturbative regime below the Kondo time. Our results highlight the role of nonequilibrium dynamics as a valuable tool in the study of quantum impurities in interacting systems.
We investigate the dynamics of a strongly correlated quantum dot system in the mixed valence regime based on the hierarchical equations of motion (HEOM) approach. The transient and steady state transport properties after a quantum quench from equilibration by rapidly applying a bias voltage in a range of temperature below and above the Kondo temperature are described. We find that the time-dependent current exhibits a linear response behavior for weak bias voltage and outside of the linear response regime for larger bias voltage due to the transition of the voltage dependent quantum dot occupancies. The influence of the temperature, finite strongly correlated electron-electron interaction and energy level of the quantum dot on the nonlinear behavior and steady state values of current indicating the Kondo physics are explored in detail.
We present a study of the correlated transport regimes of a double quantum impurity system with mutual capacitive interactions. Such system can be implemented by a double quantum dot arrangement or by a quantum dot and nearby quantum point contact, with independently connected sets of metallic terminals. Many-body spin correlations arising within each dot-lead subsystem give rise to the Kondo effect under appropriate conditions. The otherwise independent Kondo ground states may be modified by the capacitive coupling, decisively modifying the ground state of the double quantum impurity system. We analyze this coupled system through variational methods and the numerical renormalization group technique. Our results reveal a strong dependence of the coupled system ground state on the electron-hole asymmetries of the individual subsystems, as well as on their hybridization strengths to the respective reservoirs. The electrostatic repulsion produced by the capacitive coupling produces an effective shift of the individual energy levels toward higher energies, with a stronger effect on the ``shallower'' subsystem (that closer to resonance with the Fermi level), potentially pushing it out of the Kondo regime and dramatically changing the transport properties of the system. The effective remote gating that this entails is found to depend nonlinearly on the capacitive coupling strength, as well as on the independent subsystem levels. The analysis we present here of this mutual interaction should be important to fully characterize transport through such coupled systems.
An accurate and efficient numerical approach is developed for the transient electronic dynamics of open quantum systems at low temperatures. The calculations are based on a formally exact hierarchical equations of motion quantum dissipation theory [J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)]. We propose a hybrid scheme that combines the Matsubara expansion technique and a frequency dispersion treatment to account for reservoir correlation functions. The new scheme not just admits various forms of reservoir spectral functions but also greatly reduces the computational cost of the resulting hierarchical equations, especially in the low temperature regime. Dynamical Kondo effects are obtained and the cotunneling induced Kondo transitions are resolved in the transient current in response to time-dependent external voltages.
Understanding the time evolution of strongly correlated open quantum systems (OQSs) in response to perturbations (quenches) is of fundamental importance to the precise control of quantum devices. It is, however, rather challenging in multi-impurity quantum systems because such evolution often involves multiple intricate dynamical processes. In this work, we apply the numerically exact hierarchical equations of motion approach to explore the influence of two different types of perturbations, i.e., sudden swapping of the energy levels of impurity systems and activating the inter-impurity spin-exchange interaction, on the dissipation dynamics of the Kondo-correlated two-impurity Anderson model over a wide range of energetic parameters. By evaluating the time-dependent impurity spectral function and other system properties, we analyze the time evolution of the Kondo state in detail and conclude a phenomenologically scaling relation for Kondo dynamics driven by these perturbations. The evolutionary scaling relationship is not only related to the Kondo characteristic energy TK but also significantly affected by the simultaneous non-Kondo dynamic characteristic energy. We expect these results will inspire subsequent theoretical studies on the dynamics of strongly correlated OQSs.