Embedded-cluster Approximation Research Articles

Ammonium adsorption on Brønsted acidic centers on low-index vanadium pentoxide surfaces

Vanadium-based catalysts are used in many technological processes, among which the removal of nitrogen oxides (NOx) from waste gases is one of the most important. The chemical reaction responsible for this selective catalytic reaction (SCR) is based on the reduction of NOx molecules to N2, and a possible reductant in this case is pre-adsorbed NH3. In this paper, NH3 adsorption on Brønsted OH acid centers on low-index surfaces of V2O5 (010, 100, 001) is studied using a theoretical DFT method with a gradient-corrected functional (RPBE) in the embedded cluster approximation model. The results of the calculations show that ammonia molecules are spontaneously stabilized on all low-index surfaces of the investigated catalyst, with adsorption energies ranging from −0.34 to −2 eV. Two different mechanisms of ammonia adsorption occur: the predominant mechanism involves the transfer of a proton from a surface OH group and the stabilization of ammonia as an NH4 + cation bonded to surface O atom(s), while an alternative mechanism involves the hydrogen bonding of NH3 to a surface OH moiety. The latter binding mode is present only in cases of stabilization over a doubly coordinated O(2) center at a (100) surface. The results of the calculations indicate that a nondirectional local electrostatic interaction with ammonia approaching a surface predetermines the mode of stabilization, whereas hydrogen-bonding interactions are the main force stabilizing the adsorbed ammonia. Utilizing the geometric features of the hydrogen bonds, the overall strength of these interactions was quantified and qualitatively correlated (R = 0.93) with the magnitude of the stabilization effect (i.e., the adsorption energy). FigureTwo different modes (NH3/NH4 +) of ammonia adsorption on the (001)V2O5 net plane. Electronic supplementary materialThe online version of this article (doi:10.1007/s00894-013-1951-4) contains supplementary material, which is available to authorized users.

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.

Study of magnetotransport properties of interacting quantum dot systems using the ECA method

We study the magnetotransport of the interacting QD system in a magnetic field using the numerical method of embedded-cluster approximation (ECA). The spin-resolved conductances display different magnetic field dependences for different transport regimes. Through comparison of conductance polarization, the mixed-valence regime shows the largest polarization. The spin-resolved conductance as a function of the ratio between the magnetic field and Kondo temperature H/TK is found to exhibit an approximate universal behavior in the Kondo regime. We also investigate conductance dependence on interaction strength and find interesting inversion of sign of polarization in some cases.

Kondo regimes in a three-dots quantum gate

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.

Numerical analysis of the spatial range of the Kondo effect

The spatial length of the Kondo screening is still a controversial issue related to Kondo physics. While renormalization-group and Bethe-Ansatz solutions have provided detailed information about the thermodynamics of magnetic impurities, they are insufficient to study the effect on the surrounding electrons, i.e., the spatial range of the correlations created by the Kondo effect between the localized magnetic moment and the conduction electrons. The objective of this work is to present a quantitative way of measuring the extension of these correlations by studying their effect directly on the local density of states (LDOS) at arbitrary distances from the impurity. The numerical techniques used, the embedded cluster approximation, the finite-$U$ slave bosons, and numerical renormalization group, calculate the Green's functions in real space. With this information, one can calculate how the local density of states away from the impurity is modified by its presence, below and above the Kondo temperature, and then estimate the range of the disturbances in the noninteracting Fermi sea due to the Kondo effect, and how it changes with the Kondo temperature ${T}_{\text{K}}$. The results obtained agree with results obtained through spin-spin correlations, showing that the LDOS captures the phenomenology of the Kondo cloud as well.

A Perturbation Expansion Method to Study Highly Correlated Spins

This paper proposes a new numerical algorithm to study dynamical spin dependent properties of local highly correlated structures. The method consists in diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, the Embedding Cluster Approximation (ECA), combined with Wilson’s ideas of logarithmic discretization of the representation of the Hamiltonian, the Logarithm Discretization Embedded Cluster Approximation (LDECA). The physics associated to a dot and a side-coupled double dot connected to leads are discussed in detail.

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 band. A many-body formalism provides a solid theoretical foundation to the method.

Transport through quantum dots: a combined DMRG and embedded-cluster approximation 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.

Method to study highly correlated nanostructures: The logarithmic-discretization embedded-cluster approximation

This work proposes an 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.

Finite-size scaling analysis of spin correlations and fluctuations of two quantum dots in a T-shape geometry

The study of interacting nanostructures such as quantum dots is a playground for several novel numerical approaches. Recently developed methods such as the time-dependent density matrix renormalization approach or the embedded-cluster approximation rely on the numerical solution of clusters of finite-size. For the interpretation of numerical results, it is important to understand finite-size and boundary effects. Here, we study spin fluctuations and spin–spin correlations of two dots coupled in a T-shape geometry. Depending on odd–even effects, quite different results emerge from clusters that do not differ much in size.

Local-environment effects in disordered binary metallic alloys.

The electronic structure of disordered alloys is studied by means of the embedded-cluster approximation. An exact expression is obtained for the Green function for a cluster of atoms embedded in an effective medium described by the coherent-potential approximation (CPA) for an arbitrary number of dimensions and size of the cluster. This approach is applied to investigate local-environment effects in disordered alloys, including short-range order. Contrary to previous work, states are found outside of the CPA band.