Transport properties of a two impurity system: a theoretical approach

A system of two interacting cobalt atoms, at varying distances, was studied in a recent scanning tunneling microscope experiment by Bork et. al.[Nature Phys. 7, 901 (2011)]. We propose a microscopic model that explains, for all experimentally analyzed interatomic distances, the physics observed in these experiments. Our proposal is based on the two-impurity Anderson model, with the inclusion of a two-path geometry for charge transport. This many-body system is treated in the finite-U slave boson mean-field approximation and the logarithmic-discretization embedded-cluster approximation. We physically characterize the different charge transport regimes of this system at various interatomic distances and show that, as in the experiments, the features observed in the transport properties depend on the presence of two impurities but also on the existence of two conducting channels for electron transport. We interpret the splitting observed in the conductance as the result of the hybridization of the two Kondo resonances associated with each impurity.Comment: 5 pages, 5 figure

Polarized currents and spatial separation of Kondo state: NRG study of spin-orbital effect in a double QD

A double quantum dot device, connected to two channels that only see each other through interdot Coulomb repulsion, is analyzed using the numerical renormalization group technique. By using a two-impurity Anderson model, and parameter values obtained from experiment [S. Amasha {\it et al.}, Phys. Rev. Lett. {\bf 110}, 046604 (2013)], it is shown that, by applying a moderate magnetic field, and adjusting the gate potential of each quantum dot, opposing spin polarizations are created in each channel. Furthermore, through a well defined change in the gate potentials, the polarizations can be reversed. This polarization effect is clearly associated to a spin-orbital Kondo state having a Kondo peak that originates from spatially separated parts of the device. This fact opens the exciting possibility of experimentally probing the internal structure of an SU(2) Kondo state.Comment: 4+ pages; 4 figures; supplemental material (1 page, 2 figures

Transport properties of strongly correlated electrons in quantum dots using a simple circuit model

Numerical calculations are shown to reproduce the main results of recent experiments involving nonlocal spin control in nanostructures (N. J. Craig et al., Science 304, 565 (2004)). In particular, the splitting of the zero-bias-peak discovered experimentally is clearly observed in our studies. To understand these results, a simple "circuit model" is introduced and shown to provide a good qualitative description of the experiments. The main idea is that the splitting originates in a Fano anti-resonance, which is caused by having one quantum dot side-connected in relation to the current's path. This scenario provides an explanation of Craig et al.'s results that is alternative to the RKKY proposal, which is here also addressed.Comment: 5 pages, 5 figure

Transport through quantum dots: A combined DMRG and cluster-embedding study

The numerical analysis of strongly interacting nanostructures requires powerful techniques. Recently developed methods, such as the time-dependent density matrix renormalization group (tDMRG) approach or the embedded-cluster approximation (ECA), rely on the numerical solution of clusters of finite size. For the interpretation of numerical results, it is therefore crucial to understand finite-size effects in detail. In this work, we present a careful finite-size analysis for the examples of one quantum dot, as well as three serially connected quantum dots. Depending on odd-even effects, physically quite different results may emerge from clusters that do not differ much in their size. We provide a solution to a recent controversy over results obtained with ECA for three quantum dots. In particular, using the optimum clusters discussed in this paper, the parameter range in which ECA can reliably be applied is increased, as we show for the case of three quantum dots. As a practical procedure, we propose that a comparison of results for static quantities against those of quasi-exact methods, such as the ground-state density matrix renormalization group (DMRG) method or exact diagonalization, serves to identify the optimum cluster type. In the examples studied here, we find that to observe signatures of the Kondo effect in finite systems, the best clusters involving dots and leads must have a total z-component of the spin equal to zero.Comment: 16 pages, 14 figures, revised version to appear in Eur. Phys. J. B, additional reference

Transport in Carbon Nanotubes: 2LSU(2) regime reveals subtle competition between Kondo and Intermediate Valence states

In this work, we use three different numerical techniques to study the charge transport properties of a system in the two-level SU(2) (2LSU2) regime, obtained from an SU(4) model Hamiltonian by introducing orbital mixing of the degenerate orbitals via coupling to the leads. SU(4) Kondo physics has been experimentally observed, and studied in detail, in Carbon Nanotube Quantum Dots. Adopting a two molecular orbital basis, the Hamiltonian is recast into a form where one of the molecular orbitals decouples from the charge reservoir, although still interacting capacitively with the other molecular orbital. This basis transformation explains in a clear way how the charge transport in this system turns from double- to single-channel when it transitions from the SU(4) to the 2LSU2 regime. The charge occupancy of these molecular orbitals displays gate-potential-dependent occupancy oscillations that arise from a competition between the Kondo and Intermediate Valence states. The determination of whether the Kondo or the Intermediate Valence state is more favorable, for a specific value of gate potential, is assessed by the definition of an energy scale $T_0$, which is calculated through DMRG. We speculate that the calculation of $T_0$ may provide experimentalists with a useful tool to analyze correlated charge transport in many other systems. For that, a current work is underway to improve the numerical accuracy of its DRMG calculation and explore different definitions.Comment: 13 pages, 9 figure

An Exploratory Study of Forces and Frictions affecting Large-Scale Model-Driven Development

In this paper, we investigate model-driven engineering, reporting on an exploratory case-study conducted at a large automotive company. The study consisted of interviews with 20 engineers and managers working in different roles. We found that, in the context of a large organization, contextual forces dominate the cognitive issues of using model-driven technology. The four forces we identified that are likely independent of the particular abstractions chosen as the basis of software development are the need for diffing in software product lines, the needs for problem-specific languages and types, the need for live modeling in exploratory activities, and the need for point-to-point traceability between artifacts. We also identified triggers of accidental complexity, which we refer to as points of friction introduced by languages and tools. Examples of the friction points identified are insufficient support for model diffing, point-to-point traceability, and model changes at runtime.Comment: To appear in proceedings of MODELS 2012, LNCS Springe

A Novel Approach to Study Highly Correlated Nanostructures: The Logarithmic Discretization Embedded Cluster Approximation

This work proposes a new approach to study transport properties of highly correlated local structures. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilson's idea of a logarithmic discretization of the representation of the Hamiltonian. The physics associated with both one embedded dot and a double-dot side-coupled to leads is discussed in detail. In the former case, the results perfectly agree with Bethe ansatz data, while in the latter, the physics obtained is framed in the conceptual background of a two-stage Kondo problem. A many-body formalism provides a solid theoretical foundation to the method. We argue that LDECA is well suited to study complicated problems such as transport through molecules or quantum dot structures with complex ground states.Comment: 17 pages, 13 figure

Dynamic instabilities in resonant tunneling induced by a magnetic field

We show that the addition of a magnetic field parallel to the current induces self sustained intrinsic current oscillations in an asymmetric double barrier structure. The oscillations are attributed to the nonlinear dynamic coupling of the current to the charge trapped in the well, and the effect of the external field over the local density of states across the system. Our results show that the system bifurcates as the field is increased, and may transit to chaos at large enough fields.Comment: 4 pages, 3 figures, accepted in Phys. Rev. Letter

Kondo regime in triangular arrangements of quantum dots: Molecular orbitals, interference and contact effects

Transport properties of an interacting triple quantum dot system coupled to three leads in a triangular geometry has been studied in the Kondo regime. Applying mean-field finite-U slave boson and embedded cluster approximations to the calculation of transport properties unveils a set of rich features associated to the high symmetry of this system. Results using both calculation techniques yield excellent overall agreement and provide additional insights into the physical behavior of this interesting geometry. In the case when just two current leads are connected to the three-dot system, interference effects between degenerate molecular orbitals are found to strongly affect the overall conductance. An S=1 Kondo effect is also shown to appear for the perfect equilateral triangle symmetry. The introduction of a third current lead results in an `amplitude leakage' phenomenon, akin to that appearing in beam splitters, which alters the interference effects and the overall conductance through the system.Comment: 14 pages, 9 figures, submitted to PR