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Physical Review B

Effective treatment of charge and spin fluctuations in dynamical and static atom-surface interactions

Marcelo A. Romero, Fernando Flores, E. C. Goldberg

Published Dec 21, 2009• 23 citations
Publisher

Abstract

In this work we introduce a formalism that provides a good description of the correlated charge states of an atom interacting statically or dynamically with a metal surface, including realistic features of the atom-surface system. Our treatment of the Anderson impurity with an intrasite finite repulsion is based on the use of a projection operator technique and the application of the equation of motion method. The specific case of charge state configurations having zero, one, and two valence electrons of atoms with $s$-type valence orbital is discussed in this work. Static properties, such as the average occupation and the local density of states at the atom site and dynamical charge fractions in atom scattering processes, are compared with exact calculations and also with other existing approximations. Our treatment of the finite electronic repulsion at the atom site also reproduces satisfactorily the experimental behavior of the transmission phase shift of a dot measured by Aharonov-Bohm interferometry in both weak and strong coupling limits.

DOI
10.1103/physrevb.80.235427

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In this work we introduce a formalism that provides a good description of the correlated charge states of an atom interacting statically or dynamically with a metal surface, including realistic features of the atom-surface system. Our treatment of the Anderson impurity with an intrasite finite repulsion is based on the use of a projection operator technique and the application of the equation of motion method. The specific case of charge state configurations having zero, one, and two valence electrons of atoms with sss-type valence orbital is discussed in this work. Static properties, such as the average occupation and the local density of states at the atom site and dynamical charge fractions in atom scattering processes, are compared with exact calculations and also with other existing approximations. Our treatment of the finite electronic repulsion at the atom site also reproduces satisfactorily the experimental behavior of the transmission phase shift of a dot measured by Aharonov-Bohm interferometry in both weak and strong coupling limits.
This work is mainly devoted to the description of processes that involve the interaction between an atom and a surface, in which a strong Coulomb repulsion on the atomic site (U)(U)(U) limits the charge exchange to one electron (infinite-UUU limit). In this limit, the Anderson Hamiltonian for a many-fold (N)(N)(N) of states localized on the atomic site can be represented in terms of auxiliary bosons and physical operators in the mixed boson-electron space can be defined. In this work the Hamiltonian is solved by defining appropriate Green's functions for physical operators. Then we solved the equations of motion of these Green's functions, up to a second order in the atom-surface coupling, either for the stationary case or for a real time-dependent problem. We show that our approach reproduces the known exact results in the nondegenerate (N=1)(N=1)(N=1) case, and for $N\ensuremath{\succ}1$ gives excellent agreement with exact calculations and approximations valid for large NNN (the 1∕N1∕N1∕N expansion). Finally, the accurate description of dynamical processes is shown by the comparison with the exact results available for a small four-level system. In this case we also compare with results obtained by using the noncrossing approximation and with the usual spinless model calculation.
The impurity Anderson model with a finite Coulomb repulsion U has been studied by using the conventional equation-of-motion treatment for the f-electron Green's function. To get a closed equation, two types of approximations are incorporated. One is to neglect, in a large U limit, higher order Green's functions which involve three f-electron annihilation operators. The other is to linearize the equation of motion by using a projection operator method. The average valency nf{\mathit{n}}_{\mathit{f}}nf​ and the spectral density of states (DOS) of f electrons are evaluated from the self-consistent equation for the Green's function. Results for nf{\mathit{n}}_{\mathit{f}}nf​ are in good agreement with exact results of Bethe ansatz method, and the obtained spectral DOS exhibits a well-known three-peak structure. Effects of finite U and finite temperature on the spectral DOS are discussed.
A review of electronic dynamics of single-impurity and many-impurity Anderson models is contained in this report. Those models are used widely for many of the applications in diverse fields of interest, such as surface physics, theory of chemisorption and adsorbate reactions on metal surfaces, physics of intermediate valence systems, theory of heavy fermions, physics of quantum dots and other nanostructures. While standard treatments are generally based on perturbation methods, our approach is based on the non-perturbative technique for the thermodynamic Green functions. The method of the irreducible Green functions is used as the basic tool. This irreducible Green functions method allows one to describe the quasiparticle spectra with damping of the strongly correlated electron systems in a very general and natural way and to construct the relevant dynamical solution in a self-consistent way on the level of Dyson equation without decoupling the chain of the equations of motion for the Green functions. The subject matter includes the improved interpolating solution of the Anderson model. It was shown that an interpolating approximation, which simultaneously reproduces the weak-coupling limit up to second order in the interaction strength U and the strong-coupling limit up to second order in the hybridization V (and thus also fulfils the atomic limit) can be formulated self-consistently. This approach offers a new way for the systematic construction of approximate interpolation dynamical solutions of strongly correlated electron systems.
The linear Hubbard model is considered when the intrasite Coulomb repulsion is very large compared to the intersite charge-transfer interaction. The solution for a general density of electrons per site is carried out by a perturbative treatment which relates this Hubbard model to a generalized Heisenberg spin Hamiltonian describing effective exchange interactions between (partially) delocalized electrons. Accurate numerical results for the linear Heisenberg model are employed to obtain good estimates of the static thermodynamic properties for Hubbard models near the atomic limit. Some modifications of the simple Hubbard model are also briefly discussed.
Nanostructures with open shell transition metal or molecular constituents host often strong electronic correlations and are highly sensitive to atomistic material details. This tutorial review discusses method developments and applications of theoretical approaches for the realistic description of the electronic and magnetic properties of nanostructures with correlated electrons. First, the implementation of a flexible interface between density functional theory and a variant of dynamical mean field theory (DMFT) highly suitable for the simulation of complex correlated structures is explained and illustrated. On the DMFT side, this interface is largely based on recent developments of quantum Monte Carlo and exact diagonalization techniques allowing for efficient descriptions of general four fermion Coulomb interactions, reduced symmetries and spin-orbit coupling, which are explained here. With the examples of the Cr (001) surfaces, magnetic adatoms, and molecular systems it is shown how the interplay of Hubbard U and Hund’s J determines charge and spin fluctuations and how these interactions drive different sorts of correlation effects in nanosystems. Non-local interactions and correlations present a particular challenge for the theory of low dimensional systems. We present our method developments addressing these two challenges, i.e., advancements of the dynamical vertex approximation and a combination of the constrained random phase approximation with continuum medium theories. We demonstrate how non-local interaction and correlation phenomena are controlled not only by dimensionality but also by coupling to the environment which is typically important for determining the physics of nanosystems.
It is sometimes convenient to emphasize the local aspects of a part of a crystalline system, and use the corresponding localized states to build a basis of the states of the whole system. In many cases it is only a subspace of these local states that is relevant, and the Hubbard operators provide a fairly simple way to write the corresponding projected Hamiltonian. Two examples of this type of treatment are presented int this work. The first is a Co2+ impurity in a MgO crystal interacting through a Jahn-Teller term with the crystal phonons, and it is shown how this interaction affects the electronic Raman scattering. The second is the Anderson lattice when the local electrons have an infinite Coulomb repulsion, and a diagrammatic expansion with cumulants is discussed. We propose a method to obtain approximate Green's functions for the Anderson lattice that employs the exact solutions of an atomic problem, and the corresponding spectral density of the local electrons is calculated.