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Formation of the Kondo resonance in two-atom molecular systems for various interaction limits

Wojtek Iwo Babiaczyk, Bogdan R. Bułka

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

We consider a two-atom molecule connected to ferromagnetic leads, in the Kondo transport regime. To investigate the Kondo effect in the system, we use the slave–boson mean field approximation (SBMFA) techniques. Results are obtained for both the strong interaction limit, in which an infinite Coulomb repulsion U1–2 between atoms is assumed, and a finite U1–2 case. The transport is considered in the T = 0 and V = 0 equilibrium limit.

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We consider a two-atom molecule connected to ferromagnetic leads, in the Kondo transport regime. To investigate the Kondo effect in the system, we use the slave–boson mean field approximation (SBMFA) techniques. Results are obtained for both the strong interaction limit, in which an infinite Coulomb repulsion U1–2 between atoms is assumed, and a finite U1–2 case. The transport is considered in the T = 0 and V = 0 equilibrium limit.
A system of two interacting Co atoms has been studied in a recent Scanning Tunneling Microscope experiment by J. Bork et al., Nature Physics 7, 901 (2011). This kind of system has been intensively analyzed since a quantum critical point was theoretically predicted for an antiferromagnetic interacting dimer. We propose a two path structure microscopic model capable of explaining, in all the parameter space, the physics of this experiment. It consists of two atoms interacting directly and indirectly through a hopping between two electronic reservoirs that bypasses the atoms. The many-body system is treated in the finite-U Slave Boson Mean Field Approximation. Other results obtained using the Logarithmic Discretization Embedded Cluster Approximation are also discussed. The system is characterized as being in the Kondo regime for all the parameter space experimentally studied, although the effective exchange interaction between the Co atoms is antiferromagnetic.
In this document we present a study of the thermodynamic and transport properties of two kinds of quantum impurity systems in the Kondo regime.The first system consists of a spin-1 molecule in which mechanical stretching along the transport axis produces a magnetic anisotropy.We find that a generic coupling between a vibrational mode along this axis and the molecular spin induces a correction to the magnetic anisotropy, driving the ground state of the system into a non-Fermi-liquid phase.A transition into a Fermi-liquid ground state can then be induced by means of stretching, going through an underscreened spin-1 Kondo ground state at zero effective anisotropy.In the second system we study the effects of a charge detector, implemented by a quantum point-contact (QPC), on the Kondo state of a nearby spin-1/2 quantum dot (QD).While making the charge detection possible, the Coulomb interaction between the electrons traversing the QPC and those within the QD contribute to decoherence of the Kondo state.By modeling the QPC as two metallic terminals connected to an intermediate localized level, we can explore three transport regimes of the detector: a zero-conductance regime, a finite-conductance regime in mixed valence, and unitary conductance in a Kondo ground state that has been suggested as an explanation to the "0.7 anomaly" in QPCs.Transitions between these different ground states can be achieved by tuning the strength of a capacitive coupling that parameterizes the electrostatic interaction.
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 analyze the two-Anderson-impurity problem, in the strong-Coulomb-repulsion limit, by means of variational wave functions whose equations we solve analytically. We found two pairs of doublet states, one odd and one even with respect to the midplane between the impurities. These doublets make a significatively strong use of the hybridization terms of the Hamiltonian and have a much larger Kondo-like correlation energy than a single impurity (the Kondo energy). Furthermore, these doublets combine to form a supersinglet. This supersinglet makes use of the remaining hybridization probability to improve its energy with respect to the doublet energy, but for low-dimensional systems and at the interimpurity distances where the doublets are fully developed, its energy gain is exponentially small. The interaction behind the doublets is a first-order (in the effective Kondo coupling) one; it also generates a parallel alignment of the impurity spins. This ferromagnetic impurity-impurity response is thus generated without resort to the RKKY interaction. The effective range of this first-order Doublet interaction is also much larger than the one of the RKKY interaction.
Kondo physics in nonequilibrium interacting nanoscale devices is an attractive fundamental many-particle phenomenon with a rich potential for applications. Due to enormous complexity its clear and flexible theory is still highly desirable. We develop a physically transparent analytical theory capable of correctly describing the Kondo effect in strongly interacting systems at temperatures close to and above the Kondo temperature. We derive a nonequilibrium Keldysh field theory valid for a system with any finite electron-electron interaction which is much stronger than the coupling of the system to contacts. Finite electron-electron interactions are treated involving as many slave-boson degrees of freedom as one needs for a concrete many-body system. In a small vicinity of the zero slave-bosonic field configuration weak slave-bosonic oscillations, induced by the dot-contacts tunneling, are described by an effective Keldysh action quadratic in the slave-bosonic fields. For clarity the theory is presented for the single impurity Anderson model but the construction of the Keldysh field integral is universal and applicable to systems with more complex many-body spectra.