Single-impurity Anderson model

FIGURE 5.6 X-ray absorption spectrum of the Co L-edge of cobalt nanocrystals calculated from the single-impurity Anderson model, illustrating a charge transfer from metal nanocrystals to ligand molecules. Reprinted with permission from Ref. [19]. American Chemical Society. 

Very extended calculations of various physical properties (including Im ximaximum value and compared with a Lorentzian and experimental data for CePdj at 5 K from Galera et al. (1985a,b). For the... 

This resonance at ks K provides a partial explanation for the surprising temperature dependence of equilibrium and transport properties of dilute alloys and mixed-valent systems. The important conclusion emerging from the relevant theory (Bickers et al. 1985, Allen et al. 1986) is that the low-temperature susceptibility and specific heat reflect a greatly enhanced density of states proportional to IjT, not l/ p. Since these arguments are based on solution of the single-impurity Anderson model, they cannot be expected to apply a priori to concentrated systems. Nonetheless, for temperatures T > the single-impurity results, scaled by the number of impurities, seem to work for most properties. The most prominent deviation at low temperatures occurs for the resistivity, which Bloch s theorem forces to zero whereas the single-impurity result saturates (Lee et al. 1986). 

The applicability of the single-impurity Anderson model description to concentrated compounds and alloys does remain the subject of much debate. It is apparent that as the temperature is lowered, the f moments start to induce a compensating polarization cloud... 

Heavy fermion materials are usually modeled by the single impurity Anderson model or the periodic Anderson model depending on the concentration of the correlated f orbitals. Although at high temperatures the SIM captures the same physics as the lattice model, it caimot account for the electronic coherence at low temperatures. The periodic Anderson model (PAM) is believed to describe the strong correlation of f electrons as well as their... 

Fig. 13. Near-Fenni-energy structure of the hybridization function for the asymmetric PAM. The model parameters are 17 = 1.5, F = 0.6 and n, = 1. The dip at the Fermi energy denotes a decrease in the number of states available for screening, leading to a suppressed coherence Kondo scale T. The zero ten erature hybridization for the single-impurity Anderson model is shown for comparison.

Gunnarsson and Schonhammer (1983a,b,c, 1985a,b see also chapter 64 in this volume) proposed a description of Ce spectroscopic data in terms of an Anderson impurity model, which allows to extract the crucial parameters, i.e., the 4f conduction band hybridization A and the 4f occupancy from spectroscopic data. The justification for using a single-impurity Anderson Hamiltonian comes from spectroscopic data like the BIS data discussed here or photoemission and absorption data discussed in other chapters of this book. The fact that A increases, e.g., for Ce-Ni... 

Kondo models are based on the single-impurity Anderson (1961) model, which describes an f shell that is bathed in a Fermi sea of conduction electrons. The Hamiltonian, H, can be written as the sum of three terms. 

In this sense, atomic multiplet theory provides complementary information about the valence state. One can take the view that this information should be used, and then blended in some way with the conceptual framework of the Anderson single-impurity model, so that the matrix elements coupling the / electrons to the conduction band can continue to play the decisive role in determining the extent of / electron localisation. 

Description of high-energy excitations within the Anderson single-impurity model... 

As discussed by Gunnarsson and Schonhammer in chapter 64 of this book, the parameters relevant to the extended Anderson single impurity model, originally proposed in 1977 for the description of the core level lineshapes of adsorbates (see scheme in fig. 2), and now to be used to describe core level XPS data of f-electron systems, are ... 

In the case of a single site junction with two (spin-up and spin-down) states and Coulomb interaction between these states (Anderson impurity model), the linear conductance properties have been successfully studied by means of the EOM approach in the cases related to Coulomb blockade [203, 204] and the Kondo effect [205]. Later the same method was applied to some two-site models [206-209], Multi-level systems were started to be considered only recently [210,211], Besides, there are some difficulties in building the lesser GF in the nonequilibrium case (at finite bias voltages) by means of the EOM method [212-214],... 

In the limit of a single-level quantum dot (which is, however, a two-level system because of spin degeneration) we get the Anderson impurity model (AIM)... 

The Anderson impurity model is used to describe the Coulomb interaction on a single site ... 

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