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arXiv:2206.12841 · Physical review. B./Physical review. B

Nonequilibrium spintronic transport through Kondo impurities

Anand Manaparambil, Andreas Weichselbaum, Jan von Delft, Ireneusz Weymann

Published Sep 14, 2022• 9 citations
arXivHTMLPDF

Abstract

The accurate quantitative description of the nonequilibrium transport in interacting nanoscale junctions presents a formidable challenge. Tensor network methods have entered the arena as a highly competitive, versatile, and well-controlled approach. Here, in particular, the authors use a recently developed hybrid renormalization group thermofield quench approach. With this, they obtain reliable predictions for spintronic transport through a Kondo-correlated quantum dot coupled to magnetic leads in far-from-equilibrium conditions. The work focuses on the effects of the induced exchange field. As a key result, they demonstrate that an additional external magnetic field can be utilized to achieve a full Kondo revival in an out-of-equilibrium setting.

DOI
10.1103/physrevb.106.125413

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The accurate quantitative description of the nonequilibrium transport in interacting nanoscale junctions presents a formidable challenge. Tensor network methods have entered the arena as a highly competitive, versatile, and well-controlled approach. Here, in particular, the authors use a recently developed hybrid renormalization group thermofield quench approach. With this, they obtain reliable predictions for spintronic transport through a Kondo-correlated quantum dot coupled to magnetic leads in far-from-equilibrium conditions. The work focuses on the effects of the induced exchange field. As a key result, they demonstrate that an additional external magnetic field can be utilized to achieve a full Kondo revival in an out-of-equilibrium setting.
We study nonequilibrium transport through a spin-1 Kondo dot in a local magnetic field. To this end we perform a two-loop renormalization group analysis in the weak-coupling regime yielding analytic results for (i) the renormalized magnetic field and the ggg factor, (ii) the time evolution of observables and the relevant decay rates, (iii) the magnetization and anisotropy, and (iv) the current and differential conductance in the stationary state. In particular, we find that compared to a spin-1/2 Kondo dot there exist three additional decay rates resulting in an enhanced broadening of the logarithmic features observed in stationary quantities. Additionally, we study the effect of anisotropic couplings between reservoir and impurity spin.
The numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but it faces limitations for steady-state nonequilibrium, arising, e.g., due to an applied bias voltage. We show that these limitations can be overcome by describing the thermal leads using a thermofield approach, integrating out high energy modes using NRG, and then treating the nonequilibrium dynamics at low energies using a quench protocol, implemented using the time-dependent density matrix renormalization group. This yields quantitatively reliable results for the current (with errors ≲3%) down to the exponentially small energy scales characteristic of impurity models. We present results of benchmark quality for the temperature and magnetic field dependence of the zero-bias conductance peak for the single-impurity Anderson model.
Kondo physics first surfaced into the scientific world in 1934 via an unexpected observations made by a group of experimentalists, who measured the temperature-dependent resistance of gold wires in their laboratory at the University of Leiden. When decreasing the temperature below 4 Kelvin, they observed an unexpected increase of the resistance, which resulted in a resistance minimum that was not accounted for by the theoretical understanding at that time. Only 30 years later, Jun Kondo, a Japanese physicist from Tokyo, was the first to explain this curiosity, known as the Kondo effect, under the assistance of the Kondo model. Although his findings explained the increased resistance, a more fundamental problem was raised: the Kondo problem, an unphysical divergence of the resistance at very low temperatures. To solve this problem required the development of more advanced methods beyond the scope of pure perturbative methods, namely the use of renormalization group (RG) methods. More than twenty years after Kondo’s first steps towards the solution of the resistance minimum, the Kondo effect experienced a scientific revival due to the emergence of quantum dot systems in solid state physics. A quantum dot is a very localized and spatially restricted area within a metal, where only a few electrons fit in the area. The limited spatial spread constrains the possible positions for the electrons on the dot, and forces them into strong interactions with each other–they are strongly correlated. In quantum dot systems, not only the Kondo effect in equilibrium situations between the dot and its surrounding reservoirs can be studied, but also the effects of nonequilibrium situations, where a finite bias voltage drives a current through the quantum dot. However, the nonequilibrium Kondo effect is far less explored compared to its equilibrium counterpart and it requires the development of new methods beyond established equilibrium methods. To fill this gap, we use the recently developed real-time renormalization group (RTRG) method in the weak-coupling regime and its extension to the crossover regime, from weak coupling to strong coupling. Furthermore, different combinations between the number of electrons on the dot and the number of reservoirs of electrons in the surrounding metal allow for distinct physical situations, which can be studied within the framework of the RTRG method. We subsequently characterize the properties of the the overscreened, the underscreened, and the fully screened Kondo model by analyzing their physical observables and, in parts, their time evolution. The perturbative foundation of the RTRG method gives us the opportunity to gather new analytic insights for higher spin Kondo systems, on the one hand, and provides for a qualitative comparison of obtained results to various other methods and analytic results, on the other hand.
We consider the transport properties in an applied magnetic field of the spin S=1/2S=1/2S=1/2 Kondo model with ferromagnetic exchange coupling to electronic reservoirs, a description relevant for the strong-coupling limit of underscreened spin S=1S=1S=1 Kondo impurities. Because the ferromagnetic Kondo interaction is marginally irrelevant, perturbative methods should prove accurate down to low energies. For the purpose of this study, we use a combination of Majorana diagrammatic theory with density matrix numerical renormalization group simulations. In the standard case of antiferromagnetic Kondo exchange, we first show that our simple analytical technique recovers results for the T\mathcal{T}T-matrix and spin relaxation at weak coupling (above the Kondo temperature), which were previously obtained using functional renormalization tools. Considering then the ferromagnetic case, we demonstrate how the low-energy Kondo anomaly splits for arbitrary small values of the Zeeman energy, in contrast to fully screened Kondo impurities near the strong-coupling Fermi liquid fixed point, and in agreement with recent experimental findings for spin S=1S=1S=1 molecular quantum dots.
We study the effect of an external magnetic field on the transport properties of a quantum dot using a recently developed extension of the functional renormalization group approach to non-equilibrium situations. We discuss in particular the interplay and competition of the different energy scales of the dot and the magnetic field on the stationary non-equilibrium current and conductance. As rather interesting behavior we find a switching behavior of the magnetic field for intermediate correlations and bias voltage.