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arXiv:2305.01162 · Physical review. B./Physical review. B

Role of bias and tunneling asymmetries in nonlinear Fermi-liquid transport through an SU(N) quantum dot

Kazuhiko Tsutsumi, Yoshimichi Teratani, Kaiji Motoyama, Rui Sakano, Akira Oguri

Published Jul 6, 2023• 4 citations
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Abstract

We study how bias and tunneling asymmetries affect nonlinear current through a quantum dot with $N$ discrete levels in the Fermi liquid regime, using an exact low-energy expansion of the current derived up to terms of order ${V}^{3}$ with respect to the bias voltage. The expansion coefficients are described in terms of the phase shift, the linear susceptibilities, and the three-body correlation functions, defined with respect to the equilibrium ground state of the Anderson impurity model. In particular, the three-body correlations play an essential role in the order ${V}^{3}$ term, and their coupling to the nonlinear current depends crucially on the bias and tunnel asymmetries. The number of independent components of the three-body correlation functions increases with $N$ the internal degrees of the quantum dots, and it gives a variety in the low-energy transport. We calculate the correlation functions over a wide range of electron fillings of the Anderson impurity model with the $\mathrm{SU}(N)$ internal symmetry, using the numerical renormalization group. We find that the order ${V}^{3}$ nonlinear current through the $\mathrm{SU}(N)$ Kondo state, which occurs at electron fillings of 1 and $N\ensuremath{-}1$ for strong Coulomb interactions, significantly varies with the three-body contributions as tunnel asymmetries increase. Furthermore, in the valence fluctuation regime toward the empty or fully occupied impurity state, a sharp peak emerges in the coefficient of ${V}^{3}$ current in the case at which bias and tunneling asymmetries cooperatively enhance the charge transfer from one of the electrodes.

DOI
10.1103/physrevb.108.045109

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This thesis contributes to the field of transport through quantum dots. These devices allow for a controlled study of quantum transport and fundamental physical effects, like the Kondo effect. In this thesis we will focus on dots that are well described by generalized Anderson impurity models, where the discrete levels of the quantum dot are tunnel-coupled to fermionic reservoirs. The model parameters, like level energy and width, can be tuned in experiments. Therefore these systems constitute a valuable arena for testing experiment against theory and vice versa. In order to describe these strongly correlated systems, we employ the numerical renormalization group method. This allows us to address both longstanding questions concerning experimental results and new physical phenomena in these fundamental models. This thesis consists of three major projects. The first and most extensive one is concerned with the phase of the transmission amplitude through a quantum dot. Measurements of many-electron quantum dots with small level spacing reveal universal phase behaviour, a result not fully understood for almost 10 years. Recent experiments have seen that, contrarily, for dots with only a few electrons, i.e. large level spacing, the phase depends on the mesoscopic dot parameters. Analyzing a multi-level Anderson model, we show that the generic feature of the two regimes can be reproduced in the regime of overlapping levels or well separated levels, respectively. Thereby the universal character follows from Fano-type antiresonances of the renormalized single-particle levels. Moderate temperature supports the universal character. In the mesoscopic regime, we also investigate the effect of Kondo correlations on the transmission phase. In a second project we analyze a quantum dot coupled to a superconducting reservoir. In contrast to previous belief, the energy resolution of our method is not restricted by the energy scale of the superconducting gap, leading to new insights into the method. The high resolution allows us to resolve sharp peaks in the spectral function that emerge for a certain regime of parameters. A third project deals with a quantum dot coupled to two independent channels, a system known to exhibit non-Fermi liquid behaviour. We investigate the existence of the non-Fermi liquid regime when driving the system out of the Kondo regime by emptying the dot. We find that the extent of the non-Fermi liquid regime strongly depends on the mechanisms that couple impurity and reservoirs but prevent mixing of the latter.
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