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arXiv:2305.17686

Kondo regime of the impurity spectral function and the current noise spectrum in the double impurity Anderson model

Zi‐Hao Chen, YiJing Yan

Published May 28, 2023• 0 citations
arXivHTMLPDF

Abstract

The dissipaton equations of motion (DEOM) method is one of the most popular methods for simulating quantum impurity systems. In this article, we use DOEM theory to deal with the Kondo problem of the double quantum dots (DQDs) impurity system. We focus on the impurity spectral function and the total noise spectral function, this two function will be used to describe the Kondo effect of this system. The influence of the interaction, the hooping and the difference of the chemical potential between the two dots on the Kondo effect of the system is studied. We find that the interaction between the two dots can influence the Kondo effect of the system a lot.

DOI
10.48550/arxiv.2305.17686

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The dissipaton equations of motion (DEOM) method is one of the most popular methods for simulating quantum impurity systems. In this article, we use DOEM theory to deal with the Kondo problem of the double quantum dots (DQDs) impurity system. We focus on the impurity spectral function and the total noise spectral function, this two function will be used to describe the Kondo effect of this system. The influence of the interaction, the hooping and the difference of the chemical potential between the two dots on the Kondo effect of the system is studied. We find that the interaction between the two dots can influence the Kondo effect of the system a lot.
The nonequilibrium time evolution of a quantum dot is studied by means of dynamic equations for time-dependent Green's functions derived from a two-particle-irreducible (2PI) effective action for the Anderson impurity model. Coupling the dot between two leads at different voltages, the dynamics of the current through the dot is investigated. We show that the 2PI approach is capable of describing the dynamical buildup of the Kondo effect, which shows up as a sharp resonance in the spectral function, with a width exponentially suppressed in the electron self-coupling on the dot. An external voltage applied to the dot is found to deteriorate the Kondo effect at the hybridization scale. The dynamic equations are evaluated within different nonperturbative resummation schemes, within the direct, particle-particle, and particle-hole channels, as well as their combination, and the results compared with those from other methods.
The out-of-equilibrium transport properties of a double quantum dot system in the Kondo regime are studied theoretically by means of a two-impurity Anderson Hamiltonian with interimpurity hopping. The Hamiltonian is solved by means of a nonequilibrium generalization of the slave-boson mean-field theory. It is demonstrated that measurements of the differential conductance dI/dV, for appropriate values of voltages and tunneling couplings, can give a direct observation of the coherent superposition between the many-body Kondo states of each dot. For large voltages and arbitrarily large interdot tunneling, there is a critical voltage above which the physical behavior of the system again resembles that of two decoupled quantum dots.
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.
Based on the Yan's dissipaton equation of motion (DEOM) theory [J. Chem. Phys. 140, 054105 (2014)], we investigate the characteristic features of current noise spectrum in several typical transport regimes of a single-impurity Anderson model. Many well-known features such as Kondo features are correctly recovered by our DEOM calculations. More importantly, it is revealed that the intrinsic electron cotunneling process is responsible for the characteristic signature of current noise at anti-Stokes frequency. We also identify completely destructive interference in the noise spectra of noninteracting systems with two degenerate transport channels.
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.
In this paper, we present an extended dissipaton equation of motion for studying the dynamics of electronic impurity systems. Compared with the original theoretical formalism, the quadratic couplings are introduced into the Hamiltonian accounting for the interaction between the impurity and its surrounding environment. By exploiting the quadratic fermionic dissipaton algebra, the proposed extended dissipaton equation of motion offers a powerful tool for studying the dynamical behaviors of electronic impurity systems, particularly in situations where nonequilibrium and strongly correlated effects play significant roles. Numerical demonstrations are carried out to investigate the temperature dependence of the Kondo resonance in the Kondo impurity model.