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Transport properties of a two Co atoms system: a theoretical approach

Ignacio J. Hamad, L. Costa Ribeiro, George Balster Martins, E. V. Anda

Published Sep 17, 2012• 0 citations
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Abstract

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.

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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.
The transport properties of a linear structure of three quantum dots, with the central one connected to leads, are studied using the logarithmic discretization embedded cluster approximation. It is shown that the side dot spins can be ferromagnetically (F) or antiferromagnetically (AF) correlated between them, depending on the charge at the central dot. The system possesses a regime of coexistence of a two stage Kondo effect and the F phase. Ferromagnetism destroys the Kondo ground state when the system is driven to the molecular regime by increasing the interdot interaction above the largest Kondo temperature. Instead, an AF ground state does not compete with the Kondo regime. This remarkable behavior indicates that the measurement of the conductance can be an efficient readout procedure when the system operates as a quantum gate.
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.
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.
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.
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.