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arXiv:2112.08591 · Chinese Physics B

Dynamic transport characteristics of side-coupled double-quantum-impurity systems

Yijie Wang, Jianhua Wei

Published Apr 28, 2022• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1674-1056/ac6b1e

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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 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.
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.
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 investigate electronic transport through a parallel double quantum dot (DQD) system with strong on-site Coulomb interaction and capacitive interdot coupling. By applying the numerical renormalization group (NRG) method, the ground state of the system and the transmission probability at zero temperature have been obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit (2e(2)/h) due to the underscreened Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to antiferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.
A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime.
We study non-equilibrium electron transport through a quantum impurity coupled to metallic leads using the equation of motion technique at finite temperature T . Assuming that the interactions are taking place solely in the impurity and focusing on the infinite Hubbard limit, we compute the out of equilibrium density of states and the differential conductance G2(T, V ) in order to test several scaling laws. We find that G2(T, V )/G2(T, 0) is a universal function of both eV/TK and T/TK, TK being the Kondo temperature. The effect of an in-plane magnetic field on the splitting of the zero bias anomaly in the differential conductance is also analyzed. For a Zeeman splitting , the computed differential conductance peak splitting depends only on /TK, and for large fields approaches the value of 2. Besides studying the traditional two leads setup, we also consider other configurations that mimic recent experiments, namely, an impurity embedded in a mesoscopic wire and the presence of a third weakly coupled lead. In these cases, a double peak structure of the Kondo resonance is clearly obtained in the differential conductance while the amplitude of the highest peak is shown to decrease as ln(eV/TK). Several features of these results are in qualitative agreement with recent experimental observations reported on quantum dots.