Electronic correlations in double quantum dot and Anderson Impurity model

Haroon, M. A. H. Ahsan

Dafang Zheng, Wai-Sang Li, Youyan Liu

Zi‐Hao Chen, YiJing Yan

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.

Frederic W. Jayatilaka

We study the low-temperature physics arising in models of a strongly correlated, tunnel-coupled double quantum dot (DQD), particularly the two-impurity Anderson model (2AIM) and the two-impurity Kondo model (2IKM), employing a combination of physical arguments and the Numerical Renormalisation Group. These models exhibit a rich range of Kondo physics. In the regime with essentially one electron on each dot, there is a competition between the Kondo effect and the interdot exchange interaction. This competition gives rise to a quantum phase transition (QPT) between local singlet and Kondo singlet phases in the 2IKM, which becomes a continuous crossover in the 2AIM as a result of the interlead charge transfer present. The 2IKM is known to exhibit two-channel Kondo (2CK) physics at the QPT, and we investigate whether this is also the case for the 2AIM at the crossover. We find that while in principle 2CK physics can be observed in the 2AIM, extremely low temperatures are required, such that it is unlikely that 2CK physics will be observed in an experimental DQD system in the near future. We have studied the effect of a magnetic field on the 2AIM and the 2IKM, finding that both the zero-field QPT in the 2IKM and the zero-field crossover in the 2AIM, persist to finite field. This presents the possibility of observing 2CK physics in an experimental DQD at finite field, but we find that the temperatures required to do so are extremely low. We show that longer even-numbered chains of spins also exhibit QPTs at finite field, and argue that a 2N-spin chain should undergo N QPTs as field is increased (starting deep in the local singlet phase at zero field). We have also carried out a joint theoretical-experimental study of a carbon nanotube based DQD, in collaboration with Dr. Mark Buitelaar et al. The agreement between experimental and theoretical results is good, and the experiments are able to access the crossover present in the 2AIM at finite field. Furthermore, the experiments show the wide range of physics exhibited by DQD systems, and illustrate the utility of such systems in probing correlated electron physics.

Matthew Enjalran, F. Hébert, G. G. Batrouni +3 more

P. Schlottmann, Andrei A. Zvyagin

A quantum wire of finite length L with correlated electrons coupled to a quantum dot is studied. The wire is parametrized in terms of the supersymmetric $t\ensuremath{-}J$ model and the dot is represented by an Anderson-like impurity. The model is integrable and we discuss the properties of the finite chain by solving the Bethe Ansatz equations. For a finite ring the energy spectrum is discrete and has to be obtained numerically. As a function of the coupling of the dot to the wire we discuss the ground state and low-energy excitations, the Aharonov-Bohm oscillations and the discontinuities of the magnetization of the system.